TSTP Solution File: SET148-6 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET148-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:11:42 EDT 2024
% Result : Unsatisfiable 13.99s 2.35s
% Output : Refutation 13.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1295
% Syntax : Number of formulae : 4066 ( 135 unt; 0 def)
% Number of atoms : 15187 (1471 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 19784 (8663 ~;9930 |; 0 &)
% (1191 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 28 ( 4 avg)
% Number of predicates : 1203 (1201 usr;1192 prp; 0-3 aty)
% Number of functors : 39 ( 39 usr; 13 con; 0-3 aty)
% Number of variables : 5598 (5598 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27371,plain,
$false,
inference(avatar_sat_refutation,[],[f207,f212,f217,f221,f226,f230,f234,f238,f242,f247,f252,f256,f260,f265,f269,f273,f277,f281,f285,f289,f293,f297,f301,f306,f311,f316,f321,f325,f329,f333,f337,f341,f345,f349,f353,f357,f361,f374,f378,f382,f387,f391,f396,f426,f430,f434,f441,f446,f450,f454,f458,f462,f466,f470,f479,f501,f505,f509,f513,f518,f526,f530,f534,f541,f545,f554,f558,f562,f566,f570,f577,f586,f590,f594,f598,f611,f615,f626,f630,f643,f647,f652,f656,f666,f671,f675,f679,f684,f688,f693,f698,f704,f720,f725,f729,f733,f737,f741,f747,f752,f759,f763,f781,f791,f804,f813,f817,f821,f825,f886,f890,f894,f917,f921,f930,f939,f949,f953,f957,f961,f965,f987,f1006,f1010,f1014,f1018,f1022,f1026,f1085,f1089,f1093,f1097,f1106,f1110,f1157,f1161,f1165,f1169,f1173,f1223,f1232,f1241,f1245,f1249,f1275,f1279,f1288,f1292,f1296,f1300,f1318,f1322,f1353,f1363,f1367,f1371,f1375,f1379,f1446,f1450,f1454,f1458,f1466,f1475,f1479,f1517,f1525,f1532,f1545,f1551,f1558,f1580,f1586,f1599,f1611,f1616,f1622,f1641,f1658,f1662,f1706,f1713,f1747,f1775,f1795,f1805,f1810,f1814,f1870,f1908,f1915,f1925,f1937,f1947,f1996,f2000,f2053,f2058,f2069,f2082,f2095,f2099,f2112,f2122,f2126,f2139,f2141,f2225,f2229,f2259,f2263,f2267,f2279,f2289,f2307,f2313,f2336,f2344,f2349,f2354,f2358,f2362,f2366,f2374,f2379,f2383,f2391,f2396,f2404,f2412,f2416,f2426,f2435,f2446,f2450,f2454,f2458,f2469,f2481,f2492,f2497,f2501,f2505,f2521,f2527,f2531,f2542,f2560,f2687,f2691,f2701,f2707,f2711,f2713,f2725,f2729,f2733,f2737,f2741,f2749,f2812,f2816,f2820,f2824,f2828,f2833,f2854,f2907,f2918,f2925,f2932,f2937,f2942,f2947,f2951,f2955,f3044,f3055,f3063,f3068,f3073,f3094,f3108,f3120,f3139,f3143,f3147,f3151,f3155,f3164,f3168,f3174,f3178,f3183,f3189,f3195,f3203,f3212,f3216,f3220,f3224,f3308,f3312,f3326,f3330,f3334,f3460,f3468,f3474,f3480,f3484,f3493,f3500,f3504,f3508,f3512,f3517,f3523,f3527,f3531,f3535,f3539,f3543,f3547,f3597,f3616,f3747,f3755,f3759,f3763,f3767,f3771,f3775,f3779,f3783,f3787,f3791,f3800,f3804,f3808,f3812,f3816,f3820,f3824,f3828,f3832,f3836,f4200,f4204,f4209,f4213,f4217,f4221,f4225,f4229,f4233,f4237,f4241,f4245,f4250,f4251,f4259,f4268,f4272,f4367,f4643,f4738,f4765,f4769,f4775,f4780,f4784,f4788,f4792,f4796,f4800,f4805,f4809,f4814,f4818,f4822,f4826,f4830,f4834,f4847,f4851,f4856,f5141,f5145,f5172,f5461,f5470,f5477,f5482,f5487,f5497,f5503,f5508,f5512,f5520,f5525,f5530,f5538,f5542,f5546,f5550,f5554,f5558,f5563,f5570,f5578,f5809,f5818,f5879,f5885,f5890,f5894,f5898,f5903,f5908,f5917,f5921,f5925,f5929,f6018,f6022,f6180,f6185,f6189,f6194,f6206,f6210,f6214,f6222,f6228,f6232,f6236,f6400,f6404,f6408,f6412,f6417,f6422,f6431,f6435,f6439,f6443,f6447,f6451,f6455,f6463,f6595,f6599,f6805,f6810,f6814,f6818,f6822,f6826,f6830,f6834,f6844,f6992,f7004,f7008,f7012,f7016,f7020,f7024,f7028,f7033,f7037,f7049,f7357,f7361,f7365,f7369,f7382,f7390,f7395,f7400,f7424,f7433,f7438,f7442,f7446,f7456,f7460,f7464,f7468,f7472,f8138,f8142,f8146,f8151,f8156,f8160,f8186,f8193,f8202,f8209,f8220,f8224,f8228,f8232,f8236,f8299,f8303,f8310,f8315,f8319,f8323,f8337,f8341,f8345,f8349,f8353,f8357,f8669,f8704,f8708,f8712,f8716,f8720,f8724,f8728,f8815,f8819,f8827,f8831,f8835,f8839,f8848,f8855,f8982,f8986,f8990,f8994,f8999,f9003,f9064,f9078,f9092,f9096,f9103,f9110,f9115,f9120,f9125,f9131,f9141,f9184,f9188,f9192,f9196,f9200,f9204,f9208,f9235,f9328,f9332,f9339,f9346,f9351,f9355,f9360,f9367,f9372,f9380,f9392,f9396,f9457,f9515,f9519,f9527,f9583,f9657,f9666,f9673,f9680,f9684,f9691,f9695,f9699,f9716,f9720,f9761,f9765,f9769,f9773,f9777,f9781,f9903,f9909,f9917,f9925,f9931,f9939,f9944,f9948,f9952,f9956,f9960,f9964,f9968,f9972,f9976,f9980,f10362,f10369,f10373,f10442,f10446,f10546,f10550,f10554,f10562,f10595,f10599,f10603,f10780,f10785,f10790,f10795,f11021,f11025,f11029,f11033,f11037,f11041,f11444,f11448,f11453,f11472,f11476,f11569,f11573,f11607,f11624,f11629,f11640,f11646,f11652,f11735,f11739,f11753,f11757,f11785,f11789,f11865,f11894,f11898,f11902,f12101,f12105,f12109,f12151,f12156,f12161,f12165,f12170,f12178,f12184,f12188,f12192,f12196,f12590,f12595,f12600,f12604,f12608,f12612,f12992,f12996,f13000,f13004,f13008,f13012,f13016,f13142,f13146,f13442,f13466,f13528,f13532,f13563,f13567,f13571,f13638,f13642,f13774,f13778,f13782,f13858,f13862,f13956,f13960,f13964,f14015,f14019,f14023,f14027,f14250,f14265,f14323,f14327,f14331,f14335,f14507,f14511,f14515,f14519,f14603,f14633,f14686,f14694,f14701,f14709,f14807,f14842,f14846,f14850,f14855,f14994,f14998,f15003,f15187,f15210,f15218,f15223,f15228,f15236,f15251,f15260,f15266,f15270,f15274,f15282,f15287,f15291,f15498,f15502,f15508,f15512,f15541,f15545,f15550,f15555,f15559,f15563,f15567,f15578,f15582,f15664,f15668,f15727,f15734,f15768,f15772,f15776,f15792,f15855,f15863,f15868,f15876,f15881,f15885,f15889,f15893,f15897,f15993,f15997,f16013,f16017,f16038,f16046,f16230,f16234,f16280,f16297,f16301,f16364,f16368,f16376,f16382,f16403,f16408,f16412,f16533,f16538,f16542,f16547,f16551,f16556,f16561,f16565,f16569,f16594,f16598,f16602,f16720,f16724,f16728,f16732,f16736,f16925,f16970,f17011,f17015,f17019,f17023,f17042,f17046,f17099,f17219,f17227,f17231,f17235,f17382,f17387,f17392,f17533,f17576,f17604,f17621,f17631,f17636,f17648,f17652,f17656,f17660,f17670,f17703,f17717,f17721,f17725,f17729,f17733,f17737,f17741,f18104,f18108,f18112,f18167,f18199,f18203,f18401,f18405,f18455,f18576,f18715,f18719,f18781,f18825,f18830,f18834,f18898,f18902,f18906,f18910,f18914,f18918,f19163,f19243,f19247,f19251,f19256,f19261,f19265,f19269,f19479,f19486,f19490,f19540,f19546,f19596,f19600,f19604,f19667,f19712,f19716,f19742,f19746,f19750,f20081,f20085,f20263,f20267,f20298,f20321,f20370,f20374,f20378,f20422,f20426,f20477,f20499,f20503,f20507,f20529,f20533,f20568,f20572,f20624,f20770,f20784,f20788,f20793,f20797,f20847,f20851,f20923,f20928,f20932,f20963,f20967,f20971,f20975,f20979,f20983,f20987,f21006,f21291,f21309,f21314,f21326,f21343,f21373,f21403,f21417,f21485,f21490,f21520,f21553,f21618,f21622,f21718,f21722,f21727,f21732,f21737,f21741,f21746,f21751,f21755,f21759,f21763,f21768,f21772,f21776,f21781,f21786,f21790,f21794,f21798,f21802,f21806,f21810,f21814,f21818,f21822,f21826,f21830,f21834,f21838,f21842,f21846,f21850,f21855,f21860,f21865,f21870,f21875,f21880,f21884,f22077,f22713,f22738,f22747,f22769,f22770,f22891,f22897,f22902,f22911,f22915,f22919,f22924,f22937,f22941,f22945,f22959,f22963,f22967,f22971,f22975,f22979,f22983,f22987,f22992,f22996,f23011,f23015,f23019,f23023,f23027,f23186,f24035,f24039,f24043,f24048,f24052,f24057,f24066,f24070,f24074,f24078,f24082,f24086,f24091,f24096,f24100,f24104,f24109,f24114,f24118,f24122,f24126,f24131,f24135,f24140,f24144,f24148,f24152,f24156,f24160,f24164,f24168,f24172,f24176,f24180,f24184,f24188,f24192,f24197,f24201,f24205,f24210,f24215,f24473,f24868,f25431,f25575,f25580,f25584,f25588,f25595,f25604,f25611,f25616,f25629,f25650,f25654,f25658,f25662,f25666,f25670,f25674,f25678,f25682,f25698,f25702,f25706,f25710,f25714,f25718,f25722,f25726,f25730,f25734,f25739,f25743,f25748,f25752,f25756,f25761,f25766,f25770,f25775,f25788,f25794,f25800,f25804,f25808,f25989,f26318,f26735,f26949,f26953,f26960,f26968,f27358]) ).
fof(f27358,plain,
( spl0_1
| ~ spl0_1184 ),
inference(avatar_contradiction_clause,[],[f27357]) ).
fof(f27357,plain,
( $false
| spl0_1
| ~ spl0_1184 ),
inference(trivial_inequality_removal,[],[f27356]) ).
fof(f27356,plain,
( x != x
| spl0_1
| ~ spl0_1184 ),
inference(superposition,[],[f206,f25988]) ).
fof(f25988,plain,
( ! [X0] : intersection(X0,X0) = X0
| ~ spl0_1184 ),
inference(avatar_component_clause,[],[f25987]) ).
fof(f25987,plain,
( spl0_1184
<=> ! [X0] : intersection(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f206,plain,
( x != intersection(x,x)
| spl0_1 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f204,plain,
( spl0_1
<=> x = intersection(x,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f26968,plain,
( spl0_1190
| ~ spl0_1191
| ~ spl0_111
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f2569,f2499,f823,f26965,f26962]) ).
fof(f26962,plain,
( spl0_1190
<=> ! [X0,X1] : ~ member(unordered_pair(X0,X1),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f26965,plain,
( spl0_1191
<=> subclass(universal_class,complement(cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f823,plain,
( spl0_111
<=> ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f2499,plain,
( spl0_268
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(unordered_pair(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f2569,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,complement(cross_product(universal_class,universal_class)))
| ~ member(unordered_pair(X0,X1),subset_relation) )
| ~ spl0_111
| ~ spl0_268 ),
inference(resolution,[],[f2500,f824]) ).
fof(f824,plain,
( ! [X0] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,subset_relation) )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f823]) ).
fof(f2500,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(X1,X2),X0)
| ~ subclass(universal_class,complement(X0)) )
| ~ spl0_268 ),
inference(avatar_component_clause,[],[f2499]) ).
fof(f26960,plain,
( ~ spl0_1189
| spl0_344
| ~ spl0_22
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f2485,f2452,f295,f3490,f26957]) ).
fof(f26957,plain,
( spl0_1189
<=> function(complement(cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f3490,plain,
( spl0_344
<=> null_class = complement(cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f295,plain,
( spl0_22
<=> ! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f2452,plain,
( spl0_262
<=> ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f2485,plain,
( null_class = complement(cross_product(universal_class,universal_class))
| ~ function(complement(cross_product(universal_class,universal_class)))
| ~ spl0_22
| ~ spl0_262 ),
inference(resolution,[],[f2453,f296]) ).
fof(f296,plain,
( ! [X8] :
( subclass(X8,cross_product(universal_class,universal_class))
| ~ function(X8) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f2453,plain,
( ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class )
| ~ spl0_262 ),
inference(avatar_component_clause,[],[f2452]) ).
fof(f26953,plain,
( spl0_1188
| ~ spl0_38
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f2473,f2364,f372,f26951]) ).
fof(f26951,plain,
( spl0_1188
<=> ! [X0,X1] :
( subclass(identity_relation,X0)
| ~ subclass(subset_relation,X1)
| member(not_subclass_element(identity_relation,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f372,plain,
( spl0_38
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f2364,plain,
( spl0_244
<=> ! [X0] :
( member(not_subclass_element(identity_relation,X0),subset_relation)
| subclass(identity_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f2473,plain,
( ! [X0,X1] :
( subclass(identity_relation,X0)
| ~ subclass(subset_relation,X1)
| member(not_subclass_element(identity_relation,X0),X1) )
| ~ spl0_38
| ~ spl0_244 ),
inference(resolution,[],[f2365,f373]) ).
fof(f373,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f2365,plain,
( ! [X0] :
( member(not_subclass_element(identity_relation,X0),subset_relation)
| subclass(identity_relation,X0) )
| ~ spl0_244 ),
inference(avatar_component_clause,[],[f2364]) ).
fof(f26949,plain,
( spl0_1187
| ~ spl0_38
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2462,f2360,f372,f26947]) ).
fof(f26947,plain,
( spl0_1187
<=> ! [X0,X1] :
( subclass(singleton_relation,X0)
| ~ subclass(element_relation,X1)
| member(not_subclass_element(singleton_relation,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f2360,plain,
( spl0_243
<=> ! [X0] :
( member(not_subclass_element(singleton_relation,X0),element_relation)
| subclass(singleton_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f2462,plain,
( ! [X0,X1] :
( subclass(singleton_relation,X0)
| ~ subclass(element_relation,X1)
| member(not_subclass_element(singleton_relation,X0),X1) )
| ~ spl0_38
| ~ spl0_243 ),
inference(resolution,[],[f2361,f373]) ).
fof(f2361,plain,
( ! [X0] :
( member(not_subclass_element(singleton_relation,X0),element_relation)
| subclass(singleton_relation,X0) )
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f2360]) ).
fof(f26735,plain,
( spl0_1186
| ~ spl0_428
| ~ spl0_1143 ),
inference(avatar_split_clause,[],[f25888,f25582,f5479,f26732]) ).
fof(f26732,plain,
( spl0_1186
<=> singleton_relation = intersection(subset_relation,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f5479,plain,
( spl0_428
<=> subclass(singleton_relation,intersection(subset_relation,singleton_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f25582,plain,
( spl0_1143
<=> ! [X0,X1] :
( ~ subclass(X0,intersection(X1,X0))
| intersection(X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f25888,plain,
( singleton_relation = intersection(subset_relation,singleton_relation)
| ~ spl0_428
| ~ spl0_1143 ),
inference(resolution,[],[f25583,f5481]) ).
fof(f5481,plain,
( subclass(singleton_relation,intersection(subset_relation,singleton_relation))
| ~ spl0_428 ),
inference(avatar_component_clause,[],[f5479]) ).
fof(f25583,plain,
( ! [X0,X1] :
( ~ subclass(X0,intersection(X1,X0))
| intersection(X1,X0) = X0 )
| ~ spl0_1143 ),
inference(avatar_component_clause,[],[f25582]) ).
fof(f26318,plain,
( spl0_1185
| ~ spl0_420
| ~ spl0_1143 ),
inference(avatar_split_clause,[],[f25885,f25582,f4853,f26315]) ).
fof(f26315,plain,
( spl0_1185
<=> singleton_relation = intersection(element_relation,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f4853,plain,
( spl0_420
<=> subclass(singleton_relation,intersection(element_relation,singleton_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f25885,plain,
( singleton_relation = intersection(element_relation,singleton_relation)
| ~ spl0_420
| ~ spl0_1143 ),
inference(resolution,[],[f25583,f4855]) ).
fof(f4855,plain,
( subclass(singleton_relation,intersection(element_relation,singleton_relation))
| ~ spl0_420 ),
inference(avatar_component_clause,[],[f4853]) ).
fof(f25989,plain,
( spl0_1184
| ~ spl0_423
| ~ spl0_1141 ),
inference(avatar_split_clause,[],[f25809,f25573,f5170,f25987]) ).
fof(f5170,plain,
( spl0_423
<=> ! [X0] : subclass(X0,intersection(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f25573,plain,
( spl0_1141
<=> ! [X0,X1] :
( ~ subclass(X0,intersection(X0,X1))
| intersection(X0,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f25809,plain,
( ! [X0] : intersection(X0,X0) = X0
| ~ spl0_423
| ~ spl0_1141 ),
inference(resolution,[],[f25574,f5171]) ).
fof(f5171,plain,
( ! [X0] : subclass(X0,intersection(X0,X0))
| ~ spl0_423 ),
inference(avatar_component_clause,[],[f5170]) ).
fof(f25574,plain,
( ! [X0,X1] :
( ~ subclass(X0,intersection(X0,X1))
| intersection(X0,X1) = X0 )
| ~ spl0_1141 ),
inference(avatar_component_clause,[],[f25573]) ).
fof(f25808,plain,
( spl0_1183
| ~ spl0_106
| ~ spl0_686 ),
inference(avatar_split_clause,[],[f10980,f10792,f802,f25806]) ).
fof(f25806,plain,
( spl0_1183
<=> ! [X0] :
( member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f802,plain,
( spl0_106
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| member(unordered_pair(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f10792,plain,
( spl0_686
<=> not_subclass_element(cross_product(universal_class,universal_class),domain_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f10980,plain,
( ! [X0] :
( member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),X0)
| ~ subclass(universal_class,X0) )
| ~ spl0_106
| ~ spl0_686 ),
inference(superposition,[],[f803,f10794]) ).
fof(f10794,plain,
( not_subclass_element(cross_product(universal_class,universal_class),domain_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)))))
| ~ spl0_686 ),
inference(avatar_component_clause,[],[f10792]) ).
fof(f803,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X1,X2),X0)
| ~ subclass(universal_class,X0) )
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f802]) ).
fof(f25804,plain,
( spl0_1182
| ~ spl0_106
| ~ spl0_684 ),
inference(avatar_split_clause,[],[f10906,f10782,f802,f25802]) ).
fof(f25802,plain,
( spl0_1182
<=> ! [X0] :
( member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f10782,plain,
( spl0_684
<=> not_subclass_element(cross_product(universal_class,universal_class),successor_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f10906,plain,
( ! [X0] :
( member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),X0)
| ~ subclass(universal_class,X0) )
| ~ spl0_106
| ~ spl0_684 ),
inference(superposition,[],[f803,f10784]) ).
fof(f10784,plain,
( not_subclass_element(cross_product(universal_class,universal_class),successor_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)))))
| ~ spl0_684 ),
inference(avatar_component_clause,[],[f10782]) ).
fof(f25800,plain,
( spl0_1181
| ~ spl0_106
| ~ spl0_683 ),
inference(avatar_split_clause,[],[f10832,f10777,f802,f25798]) ).
fof(f25798,plain,
( spl0_1181
<=> ! [X0] :
( member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f10777,plain,
( spl0_683
<=> not_subclass_element(cross_product(universal_class,universal_class),element_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),element_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),element_relation))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f10832,plain,
( ! [X0] :
( member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),X0)
| ~ subclass(universal_class,X0) )
| ~ spl0_106
| ~ spl0_683 ),
inference(superposition,[],[f803,f10779]) ).
fof(f10779,plain,
( not_subclass_element(cross_product(universal_class,universal_class),element_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),element_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)))))
| ~ spl0_683 ),
inference(avatar_component_clause,[],[f10777]) ).
fof(f25794,plain,
( spl0_1180
| spl0_652
| ~ spl0_165
| ~ spl0_489 ),
inference(avatar_split_clause,[],[f6766,f6441,f1369,f9911,f25792]) ).
fof(f25792,plain,
( spl0_1180
<=> ! [X1] :
( ~ subclass(domain_relation,complement(X1))
| ~ subclass(domain_relation,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f9911,plain,
( spl0_652
<=> ! [X0] : ~ member(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f1369,plain,
( spl0_165
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(domain_relation,X1)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f6441,plain,
( spl0_489
<=> ! [X0,X1] :
( ~ subclass(domain_relation,complement(X0))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f6766,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(domain_relation,complement(X1))
| ~ subclass(domain_relation,X1) )
| ~ spl0_165
| ~ spl0_489 ),
inference(duplicate_literal_removal,[],[f6742]) ).
fof(f6742,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(domain_relation,complement(X1))
| ~ subclass(domain_relation,X1)
| ~ member(X0,universal_class) )
| ~ spl0_165
| ~ spl0_489 ),
inference(resolution,[],[f6442,f1370]) ).
fof(f1370,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1)
| ~ subclass(domain_relation,X1)
| ~ member(X0,universal_class) )
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f1369]) ).
fof(f6442,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0)
| ~ member(X1,universal_class)
| ~ subclass(domain_relation,complement(X0)) )
| ~ spl0_489 ),
inference(avatar_component_clause,[],[f6441]) ).
fof(f25788,plain,
( spl0_1179
| spl0_652
| ~ spl0_106
| ~ spl0_489 ),
inference(avatar_split_clause,[],[f6743,f6441,f802,f9911,f25786]) ).
fof(f25786,plain,
( spl0_1179
<=> ! [X1] :
( ~ subclass(domain_relation,complement(X1))
| ~ subclass(universal_class,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f6743,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(domain_relation,complement(X1))
| ~ subclass(universal_class,X1) )
| ~ spl0_106
| ~ spl0_489 ),
inference(resolution,[],[f6442,f803]) ).
fof(f25775,plain,
( ~ spl0_275
| spl0_1178
| ~ spl0_185
| ~ spl0_470 ),
inference(avatar_split_clause,[],[f6197,f6191,f1556,f25772,f2539]) ).
fof(f2539,plain,
( spl0_275
<=> member(regular(subset_relation),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f25772,plain,
( spl0_1178
<=> member(regular(subset_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f1556,plain,
( spl0_185
<=> ! [X0] :
( member(X0,subset_relation)
| ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f6191,plain,
( spl0_470
<=> member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f6197,plain,
( member(regular(subset_relation),subset_relation)
| ~ member(regular(subset_relation),cross_product(universal_class,universal_class))
| ~ spl0_185
| ~ spl0_470 ),
inference(resolution,[],[f6193,f1557]) ).
fof(f1557,plain,
( ! [X0] :
( ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| member(X0,subset_relation)
| ~ member(X0,cross_product(universal_class,universal_class)) )
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f1556]) ).
fof(f6193,plain,
( member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ spl0_470 ),
inference(avatar_component_clause,[],[f6191]) ).
fof(f25770,plain,
( spl0_1177
| ~ spl0_130
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f5359,f4849,f1012,f25768]) ).
fof(f25768,plain,
( spl0_1177
<=> ! [X0] :
( subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ subclass(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f1012,plain,
( spl0_130
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| member(not_subclass_element(X0,X2),X1)
| subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f4849,plain,
( spl0_419
<=> ! [X0] :
( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation)
| subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f5359,plain,
( ! [X0] :
( subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ subclass(X0,singleton_relation) )
| ~ spl0_130
| ~ spl0_419 ),
inference(duplicate_literal_removal,[],[f5348]) ).
fof(f5348,plain,
( ! [X0] :
( subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ subclass(X0,singleton_relation)
| subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_130
| ~ spl0_419 ),
inference(resolution,[],[f4850,f1013]) ).
fof(f1013,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(X0,X2),X1)
| ~ subclass(X0,X1)
| subclass(X0,X2) )
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f1012]) ).
fof(f4850,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation)
| subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_419 ),
inference(avatar_component_clause,[],[f4849]) ).
fof(f25766,plain,
( spl0_1176
| ~ spl0_130
| ~ spl0_418 ),
inference(avatar_split_clause,[],[f5335,f4845,f1012,f25764]) ).
fof(f25764,plain,
( spl0_1176
<=> ! [X0] :
( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
| ~ subclass(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f4845,plain,
( spl0_418
<=> ! [X0] :
( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
| ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(singleton_relation)))),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f5335,plain,
( ! [X0] :
( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
| ~ subclass(X0,singleton_relation) )
| ~ spl0_130
| ~ spl0_418 ),
inference(duplicate_literal_removal,[],[f5324]) ).
fof(f5324,plain,
( ! [X0] :
( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
| ~ subclass(X0,singleton_relation)
| subclass(X0,complement(compose(element_relation,complement(singleton_relation)))) )
| ~ spl0_130
| ~ spl0_418 ),
inference(resolution,[],[f4846,f1013]) ).
fof(f4846,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(singleton_relation)))),singleton_relation)
| subclass(X0,complement(compose(element_relation,complement(singleton_relation)))) )
| ~ spl0_418 ),
inference(avatar_component_clause,[],[f4845]) ).
fof(f25761,plain,
( spl0_1175
| ~ spl0_389
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f5300,f4832,f4231,f25759]) ).
fof(f25759,plain,
( spl0_1175
<=> ! [X0,X1] :
( subclass(intersection(null_class,X0),intersection(X1,null_class))
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f4231,plain,
( spl0_389
<=> ! [X2,X0,X1] :
( subclass(intersection(null_class,X0),X1)
| member(not_subclass_element(intersection(null_class,X0),X1),X2)
| null_class = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f4832,plain,
( spl0_417
<=> ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
| subclass(intersection(X0,X1),intersection(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f5300,plain,
( ! [X0,X1] :
( subclass(intersection(null_class,X0),intersection(X1,null_class))
| null_class = X1 )
| ~ spl0_389
| ~ spl0_417 ),
inference(duplicate_literal_removal,[],[f5255]) ).
fof(f5255,plain,
( ! [X0,X1] :
( subclass(intersection(null_class,X0),intersection(X1,null_class))
| subclass(intersection(null_class,X0),intersection(X1,null_class))
| null_class = X1 )
| ~ spl0_389
| ~ spl0_417 ),
inference(resolution,[],[f4833,f4232]) ).
fof(f4232,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(null_class,X0),X1),X2)
| subclass(intersection(null_class,X0),X1)
| null_class = X2 )
| ~ spl0_389 ),
inference(avatar_component_clause,[],[f4231]) ).
fof(f4833,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
| subclass(intersection(X0,X1),intersection(X2,X0)) )
| ~ spl0_417 ),
inference(avatar_component_clause,[],[f4832]) ).
fof(f25756,plain,
( spl0_1174
| ~ spl0_391
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f5299,f4832,f4239,f25754]) ).
fof(f25754,plain,
( spl0_1174
<=> ! [X0,X1] :
( subclass(intersection(X0,null_class),intersection(X1,X0))
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f4239,plain,
( spl0_391
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,null_class),X1)
| member(not_subclass_element(intersection(X0,null_class),X1),X2)
| null_class = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f5299,plain,
( ! [X0,X1] :
( subclass(intersection(X0,null_class),intersection(X1,X0))
| null_class = X1 )
| ~ spl0_391
| ~ spl0_417 ),
inference(duplicate_literal_removal,[],[f5256]) ).
fof(f5256,plain,
( ! [X0,X1] :
( subclass(intersection(X0,null_class),intersection(X1,X0))
| subclass(intersection(X0,null_class),intersection(X1,X0))
| null_class = X1 )
| ~ spl0_391
| ~ spl0_417 ),
inference(resolution,[],[f4833,f4240]) ).
fof(f4240,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,null_class),X1),X2)
| subclass(intersection(X0,null_class),X1)
| null_class = X2 )
| ~ spl0_391 ),
inference(avatar_component_clause,[],[f4239]) ).
fof(f25752,plain,
( spl0_1173
| ~ spl0_390
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f5296,f4832,f4235,f25750]) ).
fof(f25750,plain,
( spl0_1173
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,X1),intersection(X2,X0))
| ~ subclass(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f4235,plain,
( spl0_390
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,X1),X2)
| ~ subclass(X1,X3)
| member(not_subclass_element(intersection(X0,X1),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f5296,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,X1),intersection(X2,X0))
| ~ subclass(X1,X2) )
| ~ spl0_390
| ~ spl0_417 ),
inference(duplicate_literal_removal,[],[f5259]) ).
fof(f5259,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,X1),intersection(X2,X0))
| ~ subclass(X1,X2)
| subclass(intersection(X0,X1),intersection(X2,X0)) )
| ~ spl0_390
| ~ spl0_417 ),
inference(resolution,[],[f4833,f4236]) ).
fof(f4236,plain,
( ! [X2,X3,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X3)
| ~ subclass(X1,X3)
| subclass(intersection(X0,X1),X2) )
| ~ spl0_390 ),
inference(avatar_component_clause,[],[f4235]) ).
fof(f25748,plain,
( spl0_1172
| ~ spl0_388
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f5295,f4832,f4227,f25746]) ).
fof(f25746,plain,
( spl0_1172
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,X1),intersection(X2,X0))
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f4227,plain,
( spl0_388
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,X1),X2)
| ~ subclass(X0,X3)
| member(not_subclass_element(intersection(X0,X1),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f5295,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,X1),intersection(X2,X0))
| ~ subclass(X0,X2) )
| ~ spl0_388
| ~ spl0_417 ),
inference(duplicate_literal_removal,[],[f5260]) ).
fof(f5260,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,X1),intersection(X2,X0))
| ~ subclass(X0,X2)
| subclass(intersection(X0,X1),intersection(X2,X0)) )
| ~ spl0_388
| ~ spl0_417 ),
inference(resolution,[],[f4833,f4228]) ).
fof(f4228,plain,
( ! [X2,X3,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X3)
| ~ subclass(X0,X3)
| subclass(intersection(X0,X1),X2) )
| ~ spl0_388 ),
inference(avatar_component_clause,[],[f4227]) ).
fof(f25743,plain,
( spl0_1171
| ~ spl0_389
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f5235,f4828,f4231,f25741]) ).
fof(f25741,plain,
( spl0_1171
<=> ! [X0,X1] :
( subclass(intersection(null_class,X0),intersection(X1,X0))
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f4828,plain,
( spl0_416
<=> ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
| subclass(intersection(X0,X1),intersection(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f5235,plain,
( ! [X0,X1] :
( subclass(intersection(null_class,X0),intersection(X1,X0))
| null_class = X1 )
| ~ spl0_389
| ~ spl0_416 ),
inference(duplicate_literal_removal,[],[f5190]) ).
fof(f5190,plain,
( ! [X0,X1] :
( subclass(intersection(null_class,X0),intersection(X1,X0))
| subclass(intersection(null_class,X0),intersection(X1,X0))
| null_class = X1 )
| ~ spl0_389
| ~ spl0_416 ),
inference(resolution,[],[f4829,f4232]) ).
fof(f4829,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
| subclass(intersection(X0,X1),intersection(X2,X1)) )
| ~ spl0_416 ),
inference(avatar_component_clause,[],[f4828]) ).
fof(f25739,plain,
( spl0_1170
| ~ spl0_43
| ~ spl0_235
| ~ spl0_1087 ),
inference(avatar_split_clause,[],[f23937,f22990,f2310,f393,f25737]) ).
fof(f25737,plain,
( spl0_1170
<=> ! [X0] :
( subclass(singleton_relation,X0)
| ~ subclass(subset_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f393,plain,
( spl0_43
<=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f2310,plain,
( spl0_235
<=> identity_relation = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f22990,plain,
( spl0_1087
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| subclass(intersection(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f23937,plain,
( ! [X0] :
( subclass(singleton_relation,X0)
| ~ subclass(subset_relation,X0) )
| ~ spl0_43
| ~ spl0_235
| ~ spl0_1087 ),
inference(forward_demodulation,[],[f23934,f2312]) ).
fof(f2312,plain,
( identity_relation = singleton_relation
| ~ spl0_235 ),
inference(avatar_component_clause,[],[f2310]) ).
fof(f23934,plain,
( ! [X0] :
( subclass(identity_relation,X0)
| ~ subclass(subset_relation,X0) )
| ~ spl0_43
| ~ spl0_1087 ),
inference(superposition,[],[f22991,f395]) ).
fof(f395,plain,
( identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f22991,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X2,X0),X1)
| ~ subclass(X0,X1) )
| ~ spl0_1087 ),
inference(avatar_component_clause,[],[f22990]) ).
fof(f25734,plain,
( spl0_1169
| ~ spl0_391
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f5234,f4828,f4239,f25732]) ).
fof(f25732,plain,
( spl0_1169
<=> ! [X0,X1] :
( subclass(intersection(X0,null_class),intersection(X1,null_class))
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f5234,plain,
( ! [X0,X1] :
( subclass(intersection(X0,null_class),intersection(X1,null_class))
| null_class = X1 )
| ~ spl0_391
| ~ spl0_416 ),
inference(duplicate_literal_removal,[],[f5191]) ).
fof(f5191,plain,
( ! [X0,X1] :
( subclass(intersection(X0,null_class),intersection(X1,null_class))
| subclass(intersection(X0,null_class),intersection(X1,null_class))
| null_class = X1 )
| ~ spl0_391
| ~ spl0_416 ),
inference(resolution,[],[f4829,f4240]) ).
fof(f25730,plain,
( spl0_1168
| ~ spl0_390
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f5231,f4828,f4235,f25728]) ).
fof(f25728,plain,
( spl0_1168
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,X1),intersection(X2,X1))
| ~ subclass(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f5231,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,X1),intersection(X2,X1))
| ~ subclass(X1,X2) )
| ~ spl0_390
| ~ spl0_416 ),
inference(duplicate_literal_removal,[],[f5194]) ).
fof(f5194,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,X1),intersection(X2,X1))
| ~ subclass(X1,X2)
| subclass(intersection(X0,X1),intersection(X2,X1)) )
| ~ spl0_390
| ~ spl0_416 ),
inference(resolution,[],[f4829,f4236]) ).
fof(f25726,plain,
( spl0_1167
| ~ spl0_388
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f5230,f4828,f4227,f25724]) ).
fof(f25724,plain,
( spl0_1167
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,X1),intersection(X2,X1))
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f5230,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,X1),intersection(X2,X1))
| ~ subclass(X0,X2) )
| ~ spl0_388
| ~ spl0_416 ),
inference(duplicate_literal_removal,[],[f5195]) ).
fof(f5195,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,X1),intersection(X2,X1))
| ~ subclass(X0,X2)
| subclass(intersection(X0,X1),intersection(X2,X1)) )
| ~ spl0_388
| ~ spl0_416 ),
inference(resolution,[],[f4829,f4228]) ).
fof(f25722,plain,
( spl0_1166
| ~ spl0_286
| ~ spl0_397 ),
inference(avatar_split_clause,[],[f4717,f4270,f2735,f25720]) ).
fof(f25720,plain,
( spl0_1166
<=> ! [X0] :
( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),X0))
| ~ subclass(subset_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f2735,plain,
( spl0_286
<=> ! [X0] :
( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
| subclass(subset_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f4270,plain,
( spl0_397
<=> ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2))
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f4717,plain,
( ! [X0] :
( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),X0))
| ~ subclass(subset_relation,X0) )
| ~ spl0_286
| ~ spl0_397 ),
inference(duplicate_literal_removal,[],[f4681]) ).
fof(f4681,plain,
( ! [X0] :
( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),X0))
| ~ subclass(subset_relation,X0)
| subclass(subset_relation,intersection(cross_product(universal_class,universal_class),X0)) )
| ~ spl0_286
| ~ spl0_397 ),
inference(resolution,[],[f4271,f2736]) ).
fof(f2736,plain,
( ! [X0] :
( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
| subclass(subset_relation,X0) )
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f2735]) ).
fof(f4271,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2))
| ~ subclass(X0,X2) )
| ~ spl0_397 ),
inference(avatar_component_clause,[],[f4270]) ).
fof(f25718,plain,
( spl0_1165
| ~ spl0_373
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f4589,f4235,f3806,f25716]) ).
fof(f25716,plain,
( spl0_1165
<=> ! [X2,X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(intersection(X1,complement(X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f3806,plain,
( spl0_373
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,complement(X1)),X2)
| ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f4589,plain,
( ! [X2,X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(intersection(X1,complement(X0)),X2) )
| ~ spl0_373
| ~ spl0_390 ),
inference(duplicate_literal_removal,[],[f4550]) ).
fof(f4550,plain,
( ! [X2,X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(intersection(X1,complement(X0)),X2)
| subclass(intersection(X1,complement(X0)),X2) )
| ~ spl0_373
| ~ spl0_390 ),
inference(resolution,[],[f4236,f3807]) ).
fof(f3807,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1)
| subclass(intersection(X0,complement(X1)),X2) )
| ~ spl0_373 ),
inference(avatar_component_clause,[],[f3806]) ).
fof(f25714,plain,
( spl0_1164
| ~ spl0_313
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f4588,f4235,f3137,f25712]) ).
fof(f25712,plain,
( spl0_1164
<=> ! [X0,X1] :
( ~ subclass(X0,subset_relation)
| subclass(intersection(X1,X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f3137,plain,
( spl0_313
<=> ! [X0] :
( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
| subclass(X0,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f4588,plain,
( ! [X0,X1] :
( ~ subclass(X0,subset_relation)
| subclass(intersection(X1,X0),cross_product(universal_class,universal_class)) )
| ~ spl0_313
| ~ spl0_390 ),
inference(duplicate_literal_removal,[],[f4551]) ).
fof(f4551,plain,
( ! [X0,X1] :
( ~ subclass(X0,subset_relation)
| subclass(intersection(X1,X0),cross_product(universal_class,universal_class))
| subclass(intersection(X1,X0),cross_product(universal_class,universal_class)) )
| ~ spl0_313
| ~ spl0_390 ),
inference(resolution,[],[f4236,f3138]) ).
fof(f3138,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
| subclass(X0,cross_product(universal_class,universal_class)) )
| ~ spl0_313 ),
inference(avatar_component_clause,[],[f3137]) ).
fof(f25710,plain,
( spl0_1163
| ~ spl0_372
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f4494,f4227,f3802,f25708]) ).
fof(f25708,plain,
( spl0_1163
<=> ! [X2,X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(intersection(complement(X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f3802,plain,
( spl0_372
<=> ! [X2,X0,X1] :
( subclass(intersection(complement(X0),X1),X2)
| ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f4494,plain,
( ! [X2,X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(intersection(complement(X0),X1),X2) )
| ~ spl0_372
| ~ spl0_388 ),
inference(duplicate_literal_removal,[],[f4453]) ).
fof(f4453,plain,
( ! [X2,X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(intersection(complement(X0),X1),X2)
| subclass(intersection(complement(X0),X1),X2) )
| ~ spl0_372
| ~ spl0_388 ),
inference(resolution,[],[f4228,f3803]) ).
fof(f3803,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0)
| subclass(intersection(complement(X0),X1),X2) )
| ~ spl0_372 ),
inference(avatar_component_clause,[],[f3802]) ).
fof(f25706,plain,
( spl0_1162
| ~ spl0_313
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f4492,f4227,f3137,f25704]) ).
fof(f25704,plain,
( spl0_1162
<=> ! [X0,X1] :
( ~ subclass(X0,subset_relation)
| subclass(intersection(X0,X1),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f4492,plain,
( ! [X0,X1] :
( ~ subclass(X0,subset_relation)
| subclass(intersection(X0,X1),cross_product(universal_class,universal_class)) )
| ~ spl0_313
| ~ spl0_388 ),
inference(duplicate_literal_removal,[],[f4455]) ).
fof(f4455,plain,
( ! [X0,X1] :
( ~ subclass(X0,subset_relation)
| subclass(intersection(X0,X1),cross_product(universal_class,universal_class))
| subclass(intersection(X0,X1),cross_product(universal_class,universal_class)) )
| ~ spl0_313
| ~ spl0_388 ),
inference(resolution,[],[f4228,f3138]) ).
fof(f25702,plain,
( spl0_1161
| ~ spl0_352
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f3956,f3777,f3529,f25700]) ).
fof(f25700,plain,
( spl0_1161
<=> ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| null_class = intersection(X1,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f3529,plain,
( spl0_352
<=> ! [X0,X1] :
( null_class = intersection(X0,complement(X1))
| ~ member(regular(intersection(X0,complement(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f3777,plain,
( spl0_366
<=> ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| ~ subclass(X1,X2)
| member(regular(intersection(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f3956,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| null_class = intersection(X1,complement(X0)) )
| ~ spl0_352
| ~ spl0_366 ),
inference(duplicate_literal_removal,[],[f3927]) ).
fof(f3927,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| null_class = intersection(X1,complement(X0))
| null_class = intersection(X1,complement(X0)) )
| ~ spl0_352
| ~ spl0_366 ),
inference(resolution,[],[f3778,f3530]) ).
fof(f3530,plain,
( ! [X0,X1] :
( ~ member(regular(intersection(X0,complement(X1))),X1)
| null_class = intersection(X0,complement(X1)) )
| ~ spl0_352 ),
inference(avatar_component_clause,[],[f3529]) ).
fof(f3778,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(X0,X1)),X2)
| ~ subclass(X1,X2)
| intersection(X0,X1) = null_class )
| ~ spl0_366 ),
inference(avatar_component_clause,[],[f3777]) ).
fof(f25698,plain,
( spl0_1160
| ~ spl0_351
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f3890,f3769,f3525,f25696]) ).
fof(f25696,plain,
( spl0_1160
<=> ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| null_class = intersection(complement(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f3525,plain,
( spl0_351
<=> ! [X0,X1] :
( null_class = intersection(complement(X0),X1)
| ~ member(regular(intersection(complement(X0),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f3769,plain,
( spl0_364
<=> ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| ~ subclass(X0,X2)
| member(regular(intersection(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f3890,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| null_class = intersection(complement(X0),X1) )
| ~ spl0_351
| ~ spl0_364 ),
inference(duplicate_literal_removal,[],[f3859]) ).
fof(f3859,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| null_class = intersection(complement(X0),X1)
| null_class = intersection(complement(X0),X1) )
| ~ spl0_351
| ~ spl0_364 ),
inference(resolution,[],[f3770,f3526]) ).
fof(f3526,plain,
( ! [X0,X1] :
( ~ member(regular(intersection(complement(X0),X1)),X0)
| null_class = intersection(complement(X0),X1) )
| ~ spl0_351 ),
inference(avatar_component_clause,[],[f3525]) ).
fof(f3770,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(X0,X1)),X2)
| ~ subclass(X0,X2)
| intersection(X0,X1) = null_class )
| ~ spl0_364 ),
inference(avatar_component_clause,[],[f3769]) ).
fof(f25682,plain,
( spl0_1159
| ~ spl0_6
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f3742,f3614,f228,f25680]) ).
fof(f25680,plain,
( spl0_1159
<=> ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f228,plain,
( spl0_6
<=> ! [X1] : subclass(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f3614,plain,
( spl0_358
<=> ! [X0,X1] :
( ~ member(X0,singleton_relation)
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
| member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f3742,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_6
| ~ spl0_358 ),
inference(resolution,[],[f3615,f229]) ).
fof(f229,plain,
( ! [X1] : subclass(X1,X1)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f3615,plain,
( ! [X0,X1] :
( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
| ~ member(X0,singleton_relation)
| member(X0,X1) )
| ~ spl0_358 ),
inference(avatar_component_clause,[],[f3614]) ).
fof(f25678,plain,
( spl0_1158
| ~ spl0_4
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f3548,f3498,f219,f25676]) ).
fof(f25676,plain,
( spl0_1158
<=> ! [X0,X1] :
( null_class = X0
| ~ subclass(X0,X1)
| member(regular(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f219,plain,
( spl0_4
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f3498,plain,
( spl0_345
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| null_class = X0
| ~ subclass(X1,X2)
| member(regular(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f3548,plain,
( ! [X0,X1] :
( null_class = X0
| ~ subclass(X0,X1)
| member(regular(X0),universal_class) )
| ~ spl0_4
| ~ spl0_345 ),
inference(resolution,[],[f3499,f220]) ).
fof(f220,plain,
( ! [X0] : subclass(X0,universal_class)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f3499,plain,
( ! [X2,X0,X1] :
( ~ subclass(X1,X2)
| null_class = X0
| ~ subclass(X0,X1)
| member(regular(X0),X2) )
| ~ spl0_345 ),
inference(avatar_component_clause,[],[f3498]) ).
fof(f25674,plain,
( spl0_1157
| ~ spl0_130
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f3293,f3149,f1012,f25672]) ).
fof(f25672,plain,
( spl0_1157
<=> ! [X2,X0,X1] :
( subclass(X0,X1)
| ~ subclass(X0,complement(X2))
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f3149,plain,
( spl0_316
<=> ! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| subclass(X0,X2)
| ~ member(not_subclass_element(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f3293,plain,
( ! [X2,X0,X1] :
( subclass(X0,X1)
| ~ subclass(X0,complement(X2))
| ~ subclass(X0,X2) )
| ~ spl0_130
| ~ spl0_316 ),
inference(duplicate_literal_removal,[],[f3272]) ).
fof(f3272,plain,
( ! [X2,X0,X1] :
( subclass(X0,X1)
| ~ subclass(X0,complement(X2))
| ~ subclass(X0,X2)
| subclass(X0,X1) )
| ~ spl0_130
| ~ spl0_316 ),
inference(resolution,[],[f3150,f1013]) ).
fof(f3150,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,X2),X1)
| subclass(X0,X2)
| ~ subclass(X0,complement(X1)) )
| ~ spl0_316 ),
inference(avatar_component_clause,[],[f3149]) ).
fof(f25670,plain,
( spl0_1156
| ~ spl0_302
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f3290,f3149,f2940,f25668]) ).
fof(f25668,plain,
( spl0_1156
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ subclass(X0,complement(element_relation))
| ~ subclass(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f2940,plain,
( spl0_302
<=> ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f3290,plain,
( ! [X0,X1] :
( subclass(X0,X1)
| ~ subclass(X0,complement(element_relation))
| ~ subclass(X0,singleton_relation) )
| ~ spl0_302
| ~ spl0_316 ),
inference(duplicate_literal_removal,[],[f3278]) ).
fof(f3278,plain,
( ! [X0,X1] :
( subclass(X0,X1)
| ~ subclass(X0,complement(element_relation))
| subclass(X0,X1)
| ~ subclass(X0,singleton_relation) )
| ~ spl0_302
| ~ spl0_316 ),
inference(resolution,[],[f3150,f2941]) ).
fof(f2941,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,X1),element_relation)
| subclass(X0,X1)
| ~ subclass(X0,singleton_relation) )
| ~ spl0_302 ),
inference(avatar_component_clause,[],[f2940]) ).
fof(f25666,plain,
( spl0_1155
| ~ spl0_310
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f3288,f3149,f3092,f25664]) ).
fof(f25664,plain,
( spl0_1155
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ subclass(X0,complement(subset_relation))
| ~ subclass(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f3092,plain,
( spl0_310
<=> ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f3288,plain,
( ! [X0,X1] :
( subclass(X0,X1)
| ~ subclass(X0,complement(subset_relation))
| ~ subclass(X0,singleton_relation) )
| ~ spl0_310
| ~ spl0_316 ),
inference(duplicate_literal_removal,[],[f3287]) ).
fof(f3287,plain,
( ! [X0,X1] :
( subclass(X0,X1)
| ~ subclass(X0,complement(subset_relation))
| subclass(X0,X1)
| ~ subclass(X0,singleton_relation) )
| ~ spl0_310
| ~ spl0_316 ),
inference(resolution,[],[f3150,f3093]) ).
fof(f3093,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,X1),subset_relation)
| subclass(X0,X1)
| ~ subclass(X0,singleton_relation) )
| ~ spl0_310 ),
inference(avatar_component_clause,[],[f3092]) ).
fof(f25662,plain,
( spl0_1154
| ~ spl0_235
| ~ spl0_283
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3047,f2818,f2723,f2310,f25660]) ).
fof(f25660,plain,
( spl0_1154
<=> ! [X0] :
( ~ subclass(X0,singleton_relation)
| null_class = X0
| ~ subclass(X0,complement(subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f2723,plain,
( spl0_283
<=> ! [X0] :
( ~ subclass(X0,identity_relation)
| null_class = X0
| member(regular(X0),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f2818,plain,
( spl0_292
<=> ! [X0,X1] :
( ~ subclass(X0,complement(X1))
| null_class = X0
| ~ member(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f3047,plain,
( ! [X0] :
( ~ subclass(X0,singleton_relation)
| null_class = X0
| ~ subclass(X0,complement(subset_relation)) )
| ~ spl0_235
| ~ spl0_283
| ~ spl0_292 ),
inference(forward_demodulation,[],[f2987,f2312]) ).
fof(f2987,plain,
( ! [X0] :
( null_class = X0
| ~ subclass(X0,complement(subset_relation))
| ~ subclass(X0,identity_relation) )
| ~ spl0_283
| ~ spl0_292 ),
inference(duplicate_literal_removal,[],[f2982]) ).
fof(f2982,plain,
( ! [X0] :
( null_class = X0
| ~ subclass(X0,complement(subset_relation))
| null_class = X0
| ~ subclass(X0,identity_relation) )
| ~ spl0_283
| ~ spl0_292 ),
inference(resolution,[],[f2819,f2724]) ).
fof(f2724,plain,
( ! [X0] :
( member(regular(X0),subset_relation)
| null_class = X0
| ~ subclass(X0,identity_relation) )
| ~ spl0_283 ),
inference(avatar_component_clause,[],[f2723]) ).
fof(f2819,plain,
( ! [X0,X1] :
( ~ member(regular(X0),X1)
| null_class = X0
| ~ subclass(X0,complement(X1)) )
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f2818]) ).
fof(f25658,plain,
( spl0_1153
| ~ spl0_116
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f2990,f2818,f919,f25656]) ).
fof(f25656,plain,
( spl0_1153
<=> ! [X0,X1] :
( null_class = X0
| ~ subclass(X0,complement(X1))
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f919,plain,
( spl0_116
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| member(regular(X0),X1)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f2990,plain,
( ! [X0,X1] :
( null_class = X0
| ~ subclass(X0,complement(X1))
| ~ subclass(X0,X1) )
| ~ spl0_116
| ~ spl0_292 ),
inference(duplicate_literal_removal,[],[f2966]) ).
fof(f2966,plain,
( ! [X0,X1] :
( null_class = X0
| ~ subclass(X0,complement(X1))
| ~ subclass(X0,X1)
| null_class = X0 )
| ~ spl0_116
| ~ spl0_292 ),
inference(resolution,[],[f2819,f920]) ).
fof(f920,plain,
( ! [X0,X1] :
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| null_class = X0 )
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f919]) ).
fof(f25654,plain,
( spl0_1152
| ~ spl0_285
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f2988,f2818,f2731,f25652]) ).
fof(f25652,plain,
( spl0_1152
<=> ! [X0] :
( null_class = X0
| ~ subclass(X0,complement(element_relation))
| ~ subclass(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f2731,plain,
( spl0_285
<=> ! [X0] :
( ~ subclass(X0,singleton_relation)
| null_class = X0
| member(regular(X0),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f2988,plain,
( ! [X0] :
( null_class = X0
| ~ subclass(X0,complement(element_relation))
| ~ subclass(X0,singleton_relation) )
| ~ spl0_285
| ~ spl0_292 ),
inference(duplicate_literal_removal,[],[f2973]) ).
fof(f2973,plain,
( ! [X0] :
( null_class = X0
| ~ subclass(X0,complement(element_relation))
| null_class = X0
| ~ subclass(X0,singleton_relation) )
| ~ spl0_285
| ~ spl0_292 ),
inference(resolution,[],[f2819,f2732]) ).
fof(f2732,plain,
( ! [X0] :
( member(regular(X0),element_relation)
| null_class = X0
| ~ subclass(X0,singleton_relation) )
| ~ spl0_285 ),
inference(avatar_component_clause,[],[f2731]) ).
fof(f25650,plain,
( spl0_1151
| ~ spl0_124
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2871,f2310,f955,f25648]) ).
fof(f25648,plain,
( spl0_1151
<=> ! [X0] :
( member(X0,complement(compose(element_relation,complement(singleton_relation))))
| ~ member(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f955,plain,
( spl0_124
<=> ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f2871,plain,
( ! [X0] :
( member(X0,complement(compose(element_relation,complement(singleton_relation))))
| ~ member(X0,singleton_relation) )
| ~ spl0_124
| ~ spl0_235 ),
inference(superposition,[],[f956,f2312]) ).
fof(f956,plain,
( ! [X0] :
( member(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,singleton_relation) )
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f955]) ).
fof(f25629,plain,
( spl0_1150
| spl0_1148
| ~ spl0_97
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f2807,f2739,f731,f25608,f25626]) ).
fof(f25626,plain,
( spl0_1150
<=> member(not_subclass_element(universal_class,complement(singleton_relation)),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f25608,plain,
( spl0_1148
<=> subclass(universal_class,complement(singleton_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f731,plain,
( spl0_97
<=> ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f2739,plain,
( spl0_287
<=> ! [X0] :
( member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f2807,plain,
( subclass(universal_class,complement(singleton_relation))
| member(not_subclass_element(universal_class,complement(singleton_relation)),element_relation)
| ~ spl0_97
| ~ spl0_287 ),
inference(resolution,[],[f2740,f732]) ).
fof(f732,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,element_relation) )
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f731]) ).
fof(f2740,plain,
( ! [X0] :
( member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) )
| ~ spl0_287 ),
inference(avatar_component_clause,[],[f2739]) ).
fof(f25616,plain,
( spl0_1149
| ~ spl0_235
| ~ spl0_1146 ),
inference(avatar_split_clause,[],[f25606,f25597,f2310,f25613]) ).
fof(f25613,plain,
( spl0_1149
<=> member(not_subclass_element(universal_class,complement(singleton_relation)),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f25597,plain,
( spl0_1146
<=> member(not_subclass_element(universal_class,complement(identity_relation)),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f25606,plain,
( member(not_subclass_element(universal_class,complement(singleton_relation)),subset_relation)
| ~ spl0_235
| ~ spl0_1146 ),
inference(forward_demodulation,[],[f25599,f2312]) ).
fof(f25599,plain,
( member(not_subclass_element(universal_class,complement(identity_relation)),subset_relation)
| ~ spl0_1146 ),
inference(avatar_component_clause,[],[f25597]) ).
fof(f25611,plain,
( ~ spl0_1148
| ~ spl0_235
| spl0_1147 ),
inference(avatar_split_clause,[],[f25605,f25601,f2310,f25608]) ).
fof(f25601,plain,
( spl0_1147
<=> subclass(universal_class,complement(identity_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f25605,plain,
( ~ subclass(universal_class,complement(singleton_relation))
| ~ spl0_235
| spl0_1147 ),
inference(forward_demodulation,[],[f25602,f2312]) ).
fof(f25602,plain,
( ~ subclass(universal_class,complement(identity_relation))
| spl0_1147 ),
inference(avatar_component_clause,[],[f25601]) ).
fof(f25604,plain,
( spl0_1146
| spl0_1147
| ~ spl0_103
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f2805,f2739,f761,f25601,f25597]) ).
fof(f761,plain,
( spl0_103
<=> ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f2805,plain,
( subclass(universal_class,complement(identity_relation))
| member(not_subclass_element(universal_class,complement(identity_relation)),subset_relation)
| ~ spl0_103
| ~ spl0_287 ),
inference(resolution,[],[f2740,f762]) ).
fof(f762,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) )
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f761]) ).
fof(f25595,plain,
( spl0_1145
| ~ spl0_38
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f2721,f2698,f372,f25593]) ).
fof(f25593,plain,
( spl0_1145
<=> ! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f2698,plain,
( spl0_280
<=> member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f2721,plain,
( ! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),X0)
| member(null_class,X0) )
| ~ spl0_38
| ~ spl0_280 ),
inference(resolution,[],[f2700,f373]) ).
fof(f2700,plain,
( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl0_280 ),
inference(avatar_component_clause,[],[f2698]) ).
fof(f25588,plain,
( spl0_652
| spl0_1144
| ~ spl0_165
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f2561,f2499,f1369,f25586,f9911]) ).
fof(f25586,plain,
( spl0_1144
<=> ! [X0] :
( ~ subclass(universal_class,complement(X0))
| ~ subclass(domain_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f2561,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ subclass(domain_relation,X0)
| ~ member(X1,universal_class) )
| ~ spl0_165
| ~ spl0_268 ),
inference(resolution,[],[f2500,f1370]) ).
fof(f25584,plain,
( spl0_1143
| ~ spl0_39
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2243,f2227,f376,f25582]) ).
fof(f376,plain,
( spl0_39
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f2227,plain,
( spl0_224
<=> ! [X0,X1] : subclass(intersection(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f2243,plain,
( ! [X0,X1] :
( ~ subclass(X0,intersection(X1,X0))
| intersection(X1,X0) = X0 )
| ~ spl0_39
| ~ spl0_224 ),
inference(resolution,[],[f2228,f377]) ).
fof(f377,plain,
( ! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f2228,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X1)
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f2227]) ).
fof(f25580,plain,
( spl0_1142
| ~ spl0_43
| ~ spl0_235
| ~ spl0_1124 ),
inference(avatar_split_clause,[],[f25163,f24158,f2310,f393,f25577]) ).
fof(f25577,plain,
( spl0_1142
<=> subclass(singleton_relation,intersection(singleton_relation,subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f24158,plain,
( spl0_1124
<=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f25163,plain,
( subclass(singleton_relation,intersection(singleton_relation,subset_relation))
| ~ spl0_43
| ~ spl0_235
| ~ spl0_1124 ),
inference(forward_demodulation,[],[f25157,f2312]) ).
fof(f25157,plain,
( subclass(identity_relation,intersection(identity_relation,subset_relation))
| ~ spl0_43
| ~ spl0_1124 ),
inference(superposition,[],[f24159,f395]) ).
fof(f24159,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1))
| ~ spl0_1124 ),
inference(avatar_component_clause,[],[f24158]) ).
fof(f25575,plain,
( spl0_1141
| ~ spl0_39
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2232,f2223,f376,f25573]) ).
fof(f2223,plain,
( spl0_223
<=> ! [X0,X1] : subclass(intersection(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f2232,plain,
( ! [X0,X1] :
( ~ subclass(X0,intersection(X0,X1))
| intersection(X0,X1) = X0 )
| ~ spl0_39
| ~ spl0_223 ),
inference(resolution,[],[f2224,f377]) ).
fof(f2224,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X0)
| ~ spl0_223 ),
inference(avatar_component_clause,[],[f2223]) ).
fof(f25431,plain,
( spl0_1140
| ~ spl0_41
| ~ spl0_1124 ),
inference(avatar_split_clause,[],[f25150,f24158,f384,f25428]) ).
fof(f25428,plain,
( spl0_1140
<=> subclass(singleton_relation,intersection(singleton_relation,element_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f384,plain,
( spl0_41
<=> intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f25150,plain,
( subclass(singleton_relation,intersection(singleton_relation,element_relation))
| ~ spl0_41
| ~ spl0_1124 ),
inference(superposition,[],[f24159,f386]) ).
fof(f386,plain,
( intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f24868,plain,
( spl0_1139
| ~ spl0_41
| ~ spl0_1087 ),
inference(avatar_split_clause,[],[f23928,f22990,f384,f24866]) ).
fof(f24866,plain,
( spl0_1139
<=> ! [X0] :
( subclass(singleton_relation,X0)
| ~ subclass(element_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f23928,plain,
( ! [X0] :
( subclass(singleton_relation,X0)
| ~ subclass(element_relation,X0) )
| ~ spl0_41
| ~ spl0_1087 ),
inference(superposition,[],[f22991,f386]) ).
fof(f24473,plain,
( ~ spl0_1138
| spl0_805
| ~ spl0_1034 ),
inference(avatar_split_clause,[],[f22027,f21770,f15240,f24470]) ).
fof(f24470,plain,
( spl0_1138
<=> member(flip(cross_product(subset_relation,universal_class)),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f15240,plain,
( spl0_805
<=> member(domain_of(flip(cross_product(subset_relation,universal_class))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f21770,plain,
( spl0_1034
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(domain_of(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f22027,plain,
( ~ member(flip(cross_product(subset_relation,universal_class)),universal_class)
| spl0_805
| ~ spl0_1034 ),
inference(resolution,[],[f21771,f15242]) ).
fof(f15242,plain,
( ~ member(domain_of(flip(cross_product(subset_relation,universal_class))),universal_class)
| spl0_805 ),
inference(avatar_component_clause,[],[f15240]) ).
fof(f21771,plain,
( ! [X0] :
( member(domain_of(X0),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_1034 ),
inference(avatar_component_clause,[],[f21770]) ).
fof(f24215,plain,
( spl0_1137
| ~ spl0_9
| ~ spl0_735 ),
inference(avatar_split_clause,[],[f12802,f12597,f240,f24212]) ).
fof(f24212,plain,
( spl0_1137
<=> member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f240,plain,
( spl0_9
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f12597,plain,
( spl0_735
<=> not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f12802,plain,
( member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function),universal_class)
| ~ spl0_9
| ~ spl0_735 ),
inference(superposition,[],[f241,f12599]) ).
fof(f12599,plain,
( not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)))))
| ~ spl0_735 ),
inference(avatar_component_clause,[],[f12597]) ).
fof(f241,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f24210,plain,
( spl0_1136
| ~ spl0_9
| ~ spl0_734 ),
inference(avatar_split_clause,[],[f12724,f12592,f240,f24207]) ).
fof(f24207,plain,
( spl0_1136
<=> member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f12592,plain,
( spl0_734
<=> not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f12724,plain,
( member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function),universal_class)
| ~ spl0_9
| ~ spl0_734 ),
inference(superposition,[],[f241,f12594]) ).
fof(f12594,plain,
( not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)))))
| ~ spl0_734 ),
inference(avatar_component_clause,[],[f12592]) ).
fof(f24205,plain,
( spl0_1135
| ~ spl0_67
| ~ spl0_681 ),
inference(avatar_split_clause,[],[f10696,f10597,f556,f24203]) ).
fof(f24203,plain,
( spl0_1135
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,flip(cross_product(X0,X1)))
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f556,plain,
( spl0_67
<=> ! [X0,X3,X2,X1] :
( member(X3,X1)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f10597,plain,
( spl0_681
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,flip(X0))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f10696,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,flip(cross_product(X0,X1)))
| member(X2,X1) )
| ~ spl0_67
| ~ spl0_681 ),
inference(resolution,[],[f10598,f557]) ).
fof(f557,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
| member(X3,X1) )
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f10598,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0)
| ~ subclass(universal_class,flip(X0)) )
| ~ spl0_681 ),
inference(avatar_component_clause,[],[f10597]) ).
fof(f24201,plain,
( spl0_1134
| ~ spl0_67
| ~ spl0_680 ),
inference(avatar_split_clause,[],[f10611,f10593,f556,f24199]) ).
fof(f24199,plain,
( spl0_1134
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,rotate(cross_product(X0,X1)))
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f10593,plain,
( spl0_680
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,rotate(X0))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f10611,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,rotate(cross_product(X0,X1)))
| member(X2,X1) )
| ~ spl0_67
| ~ spl0_680 ),
inference(resolution,[],[f10594,f557]) ).
fof(f10594,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0)
| ~ subclass(universal_class,rotate(X0)) )
| ~ spl0_680 ),
inference(avatar_component_clause,[],[f10593]) ).
fof(f24197,plain,
( ~ spl0_1133
| ~ spl0_1022
| spl0_1029 ),
inference(avatar_split_clause,[],[f21956,f21748,f21716,f24194]) ).
fof(f24194,plain,
( spl0_1133
<=> subclass(element_relation,compose(element_relation,complement(singleton_relation))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f21716,plain,
( spl0_1022
<=> ! [X0] :
( ~ subclass(element_relation,X0)
| member(regular(singleton_relation),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f21748,plain,
( spl0_1029
<=> member(regular(singleton_relation),compose(element_relation,complement(singleton_relation))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f21956,plain,
( ~ subclass(element_relation,compose(element_relation,complement(singleton_relation)))
| ~ spl0_1022
| spl0_1029 ),
inference(resolution,[],[f21750,f21717]) ).
fof(f21717,plain,
( ! [X0] :
( member(regular(singleton_relation),X0)
| ~ subclass(element_relation,X0) )
| ~ spl0_1022 ),
inference(avatar_component_clause,[],[f21716]) ).
fof(f21750,plain,
( ~ member(regular(singleton_relation),compose(element_relation,complement(singleton_relation)))
| spl0_1029 ),
inference(avatar_component_clause,[],[f21748]) ).
fof(f24192,plain,
( spl0_1132
| ~ spl0_134
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f5364,f4849,f1083,f24190]) ).
fof(f24190,plain,
( spl0_1132
<=> ! [X0] : subclass(intersection(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f1083,plain,
( spl0_134
<=> ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f5364,plain,
( ! [X0] : subclass(intersection(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_134
| ~ spl0_419 ),
inference(duplicate_literal_removal,[],[f5343]) ).
fof(f5343,plain,
( ! [X0] :
( subclass(intersection(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(intersection(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_134
| ~ spl0_419 ),
inference(resolution,[],[f4850,f1084]) ).
fof(f1084,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1083]) ).
fof(f24188,plain,
( spl0_1131
| ~ spl0_135
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f5362,f4849,f1087,f24186]) ).
fof(f24186,plain,
( spl0_1131
<=> ! [X0] : subclass(intersection(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f1087,plain,
( spl0_135
<=> ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f5362,plain,
( ! [X0] : subclass(intersection(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_135
| ~ spl0_419 ),
inference(duplicate_literal_removal,[],[f5345]) ).
fof(f5345,plain,
( ! [X0] :
( subclass(intersection(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(intersection(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_135
| ~ spl0_419 ),
inference(resolution,[],[f4850,f1088]) ).
fof(f1088,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) )
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1087]) ).
fof(f24184,plain,
( spl0_1130
| ~ spl0_134
| ~ spl0_418 ),
inference(avatar_split_clause,[],[f5340,f4845,f1083,f24182]) ).
fof(f24182,plain,
( spl0_1130
<=> ! [X0] : subclass(intersection(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f5340,plain,
( ! [X0] : subclass(intersection(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
| ~ spl0_134
| ~ spl0_418 ),
inference(duplicate_literal_removal,[],[f5319]) ).
fof(f5319,plain,
( ! [X0] :
( subclass(intersection(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
| subclass(intersection(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation)))) )
| ~ spl0_134
| ~ spl0_418 ),
inference(resolution,[],[f4846,f1084]) ).
fof(f24180,plain,
( spl0_1129
| ~ spl0_135
| ~ spl0_418 ),
inference(avatar_split_clause,[],[f5338,f4845,f1087,f24178]) ).
fof(f24178,plain,
( spl0_1129
<=> ! [X0] : subclass(intersection(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f5338,plain,
( ! [X0] : subclass(intersection(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
| ~ spl0_135
| ~ spl0_418 ),
inference(duplicate_literal_removal,[],[f5321]) ).
fof(f5321,plain,
( ! [X0] :
( subclass(intersection(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
| subclass(intersection(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation)))) )
| ~ spl0_135
| ~ spl0_418 ),
inference(resolution,[],[f4846,f1088]) ).
fof(f24176,plain,
( spl0_1128
| ~ spl0_27
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f5304,f4832,f319,f24174]) ).
fof(f24174,plain,
( spl0_1128
<=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f319,plain,
( spl0_27
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f5304,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X0))
| ~ spl0_27
| ~ spl0_417 ),
inference(duplicate_literal_removal,[],[f5251]) ).
fof(f5251,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),intersection(intersection(X0,X1),X0))
| subclass(intersection(X0,X1),intersection(intersection(X0,X1),X0)) )
| ~ spl0_27
| ~ spl0_417 ),
inference(resolution,[],[f4833,f320]) ).
fof(f320,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f24172,plain,
( spl0_1127
| ~ spl0_407
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f5302,f4832,f4790,f24170]) ).
fof(f24170,plain,
( spl0_1127
<=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f4790,plain,
( spl0_407
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f5302,plain,
( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X1,X0))
| ~ spl0_407
| ~ spl0_417 ),
inference(duplicate_literal_removal,[],[f5253]) ).
fof(f5253,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,intersection(X1,X2)),intersection(X1,X0))
| subclass(intersection(X0,intersection(X1,X2)),intersection(X1,X0)) )
| ~ spl0_407
| ~ spl0_417 ),
inference(resolution,[],[f4833,f4791]) ).
fof(f4791,plain,
( ! [X2,X3,X0,X1] :
( member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1)
| subclass(intersection(X0,intersection(X1,X2)),X3) )
| ~ spl0_407 ),
inference(avatar_component_clause,[],[f4790]) ).
fof(f24168,plain,
( spl0_1126
| ~ spl0_406
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f5297,f4832,f4786,f24166]) ).
fof(f24166,plain,
( spl0_1126
<=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f4786,plain,
( spl0_406
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f5297,plain,
( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X2,X0))
| ~ spl0_406
| ~ spl0_417 ),
inference(duplicate_literal_removal,[],[f5258]) ).
fof(f5258,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,intersection(X1,X2)),intersection(X2,X0))
| subclass(intersection(X0,intersection(X1,X2)),intersection(X2,X0)) )
| ~ spl0_406
| ~ spl0_417 ),
inference(resolution,[],[f4833,f4787]) ).
fof(f4787,plain,
( ! [X2,X3,X0,X1] :
( member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2)
| subclass(intersection(X0,intersection(X1,X2)),X3) )
| ~ spl0_406 ),
inference(avatar_component_clause,[],[f4786]) ).
fof(f24164,plain,
( spl0_1125
| ~ spl0_405
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f5240,f4828,f4782,f24162]) ).
fof(f24162,plain,
( spl0_1125
<=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f4782,plain,
( spl0_405
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f5240,plain,
( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X0,X2))
| ~ spl0_405
| ~ spl0_416 ),
inference(duplicate_literal_removal,[],[f5185]) ).
fof(f5185,plain,
( ! [X2,X0,X1] :
( subclass(intersection(intersection(X0,X1),X2),intersection(X0,X2))
| subclass(intersection(intersection(X0,X1),X2),intersection(X0,X2)) )
| ~ spl0_405
| ~ spl0_416 ),
inference(resolution,[],[f4829,f4783]) ).
fof(f4783,plain,
( ! [X2,X3,X0,X1] :
( member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0)
| subclass(intersection(intersection(X0,X1),X2),X3) )
| ~ spl0_405 ),
inference(avatar_component_clause,[],[f4782]) ).
fof(f24160,plain,
( spl0_1124
| ~ spl0_27
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f5239,f4828,f319,f24158]) ).
fof(f5239,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1))
| ~ spl0_27
| ~ spl0_416 ),
inference(duplicate_literal_removal,[],[f5186]) ).
fof(f5186,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1))
| subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1)) )
| ~ spl0_27
| ~ spl0_416 ),
inference(resolution,[],[f4829,f320]) ).
fof(f24156,plain,
( spl0_1123
| ~ spl0_404
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f5236,f4828,f4778,f24154]) ).
fof(f24154,plain,
( spl0_1123
<=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f4778,plain,
( spl0_404
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f5236,plain,
( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X1,X2))
| ~ spl0_404
| ~ spl0_416 ),
inference(duplicate_literal_removal,[],[f5189]) ).
fof(f5189,plain,
( ! [X2,X0,X1] :
( subclass(intersection(intersection(X0,X1),X2),intersection(X1,X2))
| subclass(intersection(intersection(X0,X1),X2),intersection(X1,X2)) )
| ~ spl0_404
| ~ spl0_416 ),
inference(resolution,[],[f4829,f4779]) ).
fof(f4779,plain,
( ! [X2,X3,X0,X1] :
( member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1)
| subclass(intersection(intersection(X0,X1),X2),X3) )
| ~ spl0_404 ),
inference(avatar_component_clause,[],[f4778]) ).
fof(f24152,plain,
( spl0_1122
| ~ spl0_313
| ~ spl0_407 ),
inference(avatar_split_clause,[],[f5075,f4790,f3137,f24150]) ).
fof(f24150,plain,
( spl0_1122
<=> ! [X0,X1] : subclass(intersection(X0,intersection(subset_relation,X1)),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f5075,plain,
( ! [X0,X1] : subclass(intersection(X0,intersection(subset_relation,X1)),cross_product(universal_class,universal_class))
| ~ spl0_313
| ~ spl0_407 ),
inference(duplicate_literal_removal,[],[f5035]) ).
fof(f5035,plain,
( ! [X0,X1] :
( subclass(intersection(X0,intersection(subset_relation,X1)),cross_product(universal_class,universal_class))
| subclass(intersection(X0,intersection(subset_relation,X1)),cross_product(universal_class,universal_class)) )
| ~ spl0_313
| ~ spl0_407 ),
inference(resolution,[],[f4791,f3138]) ).
fof(f24148,plain,
( spl0_1121
| ~ spl0_313
| ~ spl0_406 ),
inference(avatar_split_clause,[],[f5017,f4786,f3137,f24146]) ).
fof(f24146,plain,
( spl0_1121
<=> ! [X0,X1] : subclass(intersection(X0,intersection(X1,subset_relation)),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f5017,plain,
( ! [X0,X1] : subclass(intersection(X0,intersection(X1,subset_relation)),cross_product(universal_class,universal_class))
| ~ spl0_313
| ~ spl0_406 ),
inference(duplicate_literal_removal,[],[f4977]) ).
fof(f4977,plain,
( ! [X0,X1] :
( subclass(intersection(X0,intersection(X1,subset_relation)),cross_product(universal_class,universal_class))
| subclass(intersection(X0,intersection(X1,subset_relation)),cross_product(universal_class,universal_class)) )
| ~ spl0_313
| ~ spl0_406 ),
inference(resolution,[],[f4787,f3138]) ).
fof(f24144,plain,
( spl0_1120
| ~ spl0_313
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f4958,f4782,f3137,f24142]) ).
fof(f24142,plain,
( spl0_1120
<=> ! [X0,X1] : subclass(intersection(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f4958,plain,
( ! [X0,X1] : subclass(intersection(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class))
| ~ spl0_313
| ~ spl0_405 ),
inference(duplicate_literal_removal,[],[f4918]) ).
fof(f4918,plain,
( ! [X0,X1] :
( subclass(intersection(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class))
| subclass(intersection(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class)) )
| ~ spl0_313
| ~ spl0_405 ),
inference(resolution,[],[f4783,f3138]) ).
fof(f24140,plain,
( spl0_1119
| ~ spl0_313
| ~ spl0_404 ),
inference(avatar_split_clause,[],[f4900,f4778,f3137,f24138]) ).
fof(f24138,plain,
( spl0_1119
<=> ! [X0,X1] : subclass(intersection(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f4900,plain,
( ! [X0,X1] : subclass(intersection(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class))
| ~ spl0_313
| ~ spl0_404 ),
inference(duplicate_literal_removal,[],[f4860]) ).
fof(f4860,plain,
( ! [X0,X1] :
( subclass(intersection(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class))
| subclass(intersection(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class)) )
| ~ spl0_313
| ~ spl0_404 ),
inference(resolution,[],[f4779,f3138]) ).
fof(f24135,plain,
( spl0_1118
| ~ spl0_372
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f4633,f4239,f3802,f24133]) ).
fof(f24133,plain,
( spl0_1118
<=> ! [X0,X1] :
( subclass(intersection(complement(X0),null_class),X1)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f4633,plain,
( ! [X0,X1] :
( subclass(intersection(complement(X0),null_class),X1)
| null_class = X0 )
| ~ spl0_372
| ~ spl0_391 ),
inference(duplicate_literal_removal,[],[f4599]) ).
fof(f4599,plain,
( ! [X0,X1] :
( subclass(intersection(complement(X0),null_class),X1)
| null_class = X0
| subclass(intersection(complement(X0),null_class),X1) )
| ~ spl0_372
| ~ spl0_391 ),
inference(resolution,[],[f4240,f3803]) ).
fof(f24131,plain,
( spl0_1117
| ~ spl0_372
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f4590,f4235,f3802,f24129]) ).
fof(f24129,plain,
( spl0_1117
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| subclass(intersection(complement(X1),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f4590,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| subclass(intersection(complement(X1),X0),X2) )
| ~ spl0_372
| ~ spl0_390 ),
inference(duplicate_literal_removal,[],[f4549]) ).
fof(f4549,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| subclass(intersection(complement(X1),X0),X2)
| subclass(intersection(complement(X1),X0),X2) )
| ~ spl0_372
| ~ spl0_390 ),
inference(resolution,[],[f4236,f3803]) ).
fof(f24126,plain,
( spl0_1116
| ~ spl0_373
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f4540,f4231,f3806,f24124]) ).
fof(f24124,plain,
( spl0_1116
<=> ! [X0,X1] :
( subclass(intersection(null_class,complement(X0)),X1)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f4540,plain,
( ! [X0,X1] :
( subclass(intersection(null_class,complement(X0)),X1)
| null_class = X0 )
| ~ spl0_373
| ~ spl0_389 ),
inference(duplicate_literal_removal,[],[f4506]) ).
fof(f4506,plain,
( ! [X0,X1] :
( subclass(intersection(null_class,complement(X0)),X1)
| null_class = X0
| subclass(intersection(null_class,complement(X0)),X1) )
| ~ spl0_373
| ~ spl0_389 ),
inference(resolution,[],[f4232,f3807]) ).
fof(f24122,plain,
( spl0_1115
| ~ spl0_373
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f4493,f4227,f3806,f24120]) ).
fof(f24120,plain,
( spl0_1115
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| subclass(intersection(X0,complement(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f4493,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| subclass(intersection(X0,complement(X1)),X2) )
| ~ spl0_373
| ~ spl0_388 ),
inference(duplicate_literal_removal,[],[f4454]) ).
fof(f4454,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| subclass(intersection(X0,complement(X1)),X2)
| subclass(intersection(X0,complement(X1)),X2) )
| ~ spl0_373
| ~ spl0_388 ),
inference(resolution,[],[f4228,f3807]) ).
fof(f24118,plain,
( spl0_1114
| ~ spl0_351
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f3957,f3777,f3525,f24116]) ).
fof(f24116,plain,
( spl0_1114
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| null_class = intersection(complement(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f3957,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| null_class = intersection(complement(X1),X0) )
| ~ spl0_351
| ~ spl0_366 ),
inference(duplicate_literal_removal,[],[f3926]) ).
fof(f3926,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| null_class = intersection(complement(X1),X0)
| null_class = intersection(complement(X1),X0) )
| ~ spl0_351
| ~ spl0_366 ),
inference(resolution,[],[f3778,f3526]) ).
fof(f24114,plain,
( spl0_1113
| ~ spl0_352
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f3889,f3769,f3529,f24112]) ).
fof(f24112,plain,
( spl0_1113
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| null_class = intersection(X0,complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f3889,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| null_class = intersection(X0,complement(X1)) )
| ~ spl0_352
| ~ spl0_364 ),
inference(duplicate_literal_removal,[],[f3860]) ).
fof(f3860,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| null_class = intersection(X0,complement(X1))
| null_class = intersection(X0,complement(X1)) )
| ~ spl0_352
| ~ spl0_364 ),
inference(resolution,[],[f3770,f3530]) ).
fof(f24109,plain,
( spl0_1112
| ~ spl0_134
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f3592,f3506,f1083,f24107]) ).
fof(f24107,plain,
( spl0_1112
<=> ! [X0,X1] :
( null_class = X0
| subclass(intersection(null_class,X1),regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f3506,plain,
( spl0_347
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,regular(X1)),null_class)
| null_class = X1
| subclass(X0,regular(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f3592,plain,
( ! [X0,X1] :
( null_class = X0
| subclass(intersection(null_class,X1),regular(X0)) )
| ~ spl0_134
| ~ spl0_347 ),
inference(duplicate_literal_removal,[],[f3583]) ).
fof(f3583,plain,
( ! [X0,X1] :
( null_class = X0
| subclass(intersection(null_class,X1),regular(X0))
| subclass(intersection(null_class,X1),regular(X0)) )
| ~ spl0_134
| ~ spl0_347 ),
inference(resolution,[],[f3507,f1084]) ).
fof(f3507,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,regular(X1)),null_class)
| null_class = X1
| subclass(X0,regular(X1)) )
| ~ spl0_347 ),
inference(avatar_component_clause,[],[f3506]) ).
fof(f24104,plain,
( spl0_1111
| ~ spl0_135
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f3591,f3506,f1087,f24102]) ).
fof(f24102,plain,
( spl0_1111
<=> ! [X0,X1] :
( null_class = X0
| subclass(intersection(X1,null_class),regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f3591,plain,
( ! [X0,X1] :
( null_class = X0
| subclass(intersection(X1,null_class),regular(X0)) )
| ~ spl0_135
| ~ spl0_347 ),
inference(duplicate_literal_removal,[],[f3584]) ).
fof(f3584,plain,
( ! [X0,X1] :
( null_class = X0
| subclass(intersection(X1,null_class),regular(X0))
| subclass(intersection(X1,null_class),regular(X0)) )
| ~ spl0_135
| ~ spl0_347 ),
inference(resolution,[],[f3507,f1088]) ).
fof(f24100,plain,
( spl0_1110
| ~ spl0_327
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f3448,f3332,f3210,f24098]) ).
fof(f24098,plain,
( spl0_1110
<=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,intersection(X0,singleton_relation))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f3210,plain,
( spl0_327
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f3332,plain,
( spl0_335
<=> ! [X0,X1] :
( member(not_subclass_element(intersection(X0,singleton_relation),X1),subset_relation)
| subclass(intersection(X0,singleton_relation),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f3448,plain,
( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,intersection(X0,singleton_relation)))
| ~ spl0_327
| ~ spl0_335 ),
inference(duplicate_literal_removal,[],[f3443]) ).
fof(f3443,plain,
( ! [X0] :
( subclass(intersection(X0,singleton_relation),intersection(subset_relation,intersection(X0,singleton_relation)))
| subclass(intersection(X0,singleton_relation),intersection(subset_relation,intersection(X0,singleton_relation))) )
| ~ spl0_327
| ~ spl0_335 ),
inference(resolution,[],[f3333,f3211]) ).
fof(f3211,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0)) )
| ~ spl0_327 ),
inference(avatar_component_clause,[],[f3210]) ).
fof(f3333,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(X0,singleton_relation),X1),subset_relation)
| subclass(intersection(X0,singleton_relation),X1) )
| ~ spl0_335 ),
inference(avatar_component_clause,[],[f3332]) ).
fof(f24096,plain,
( spl0_1109
| ~ spl0_327
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f3434,f3328,f3210,f24093]) ).
fof(f24093,plain,
( spl0_1109
<=> subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),singleton_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f3328,plain,
( spl0_334
<=> ! [X0] :
( subclass(singleton_relation,X0)
| member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f3434,plain,
( subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),singleton_relation))
| ~ spl0_327
| ~ spl0_334 ),
inference(duplicate_literal_removal,[],[f3429]) ).
fof(f3429,plain,
( subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),singleton_relation))
| subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),singleton_relation))
| ~ spl0_327
| ~ spl0_334 ),
inference(resolution,[],[f3329,f3211]) ).
fof(f3329,plain,
( ! [X0] :
( member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(singleton_relation,X0) )
| ~ spl0_334 ),
inference(avatar_component_clause,[],[f3328]) ).
fof(f24091,plain,
( spl0_1108
| ~ spl0_327
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f3422,f3324,f3210,f24088]) ).
fof(f24088,plain,
( spl0_1108
<=> subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),singleton_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f3324,plain,
( spl0_333
<=> ! [X0] :
( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
| subclass(singleton_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f3422,plain,
( subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),singleton_relation))
| ~ spl0_327
| ~ spl0_333 ),
inference(duplicate_literal_removal,[],[f3417]) ).
fof(f3417,plain,
( subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),singleton_relation))
| subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),singleton_relation))
| ~ spl0_327
| ~ spl0_333 ),
inference(resolution,[],[f3325,f3211]) ).
fof(f3325,plain,
( ! [X0] :
( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
| subclass(singleton_relation,X0) )
| ~ spl0_333 ),
inference(avatar_component_clause,[],[f3324]) ).
fof(f24086,plain,
( spl0_1107
| ~ spl0_327
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f3409,f3310,f3210,f24084]) ).
fof(f24084,plain,
( spl0_1107
<=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,intersection(singleton_relation,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f3310,plain,
( spl0_332
<=> ! [X0,X1] :
( member(not_subclass_element(intersection(singleton_relation,X0),X1),subset_relation)
| subclass(intersection(singleton_relation,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f3409,plain,
( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,intersection(singleton_relation,X0)))
| ~ spl0_327
| ~ spl0_332 ),
inference(duplicate_literal_removal,[],[f3404]) ).
fof(f3404,plain,
( ! [X0] :
( subclass(intersection(singleton_relation,X0),intersection(subset_relation,intersection(singleton_relation,X0)))
| subclass(intersection(singleton_relation,X0),intersection(subset_relation,intersection(singleton_relation,X0))) )
| ~ spl0_327
| ~ spl0_332 ),
inference(resolution,[],[f3311,f3211]) ).
fof(f3311,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(singleton_relation,X0),X1),subset_relation)
| subclass(intersection(singleton_relation,X0),X1) )
| ~ spl0_332 ),
inference(avatar_component_clause,[],[f3310]) ).
fof(f24082,plain,
( spl0_1106
| ~ spl0_134
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f3379,f3210,f1083,f24080]) ).
fof(f24080,plain,
( spl0_1106
<=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X0,intersection(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f3379,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X0,intersection(X0,X1)))
| ~ spl0_134
| ~ spl0_327 ),
inference(duplicate_literal_removal,[],[f3346]) ).
fof(f3346,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),intersection(X0,intersection(X0,X1)))
| subclass(intersection(X0,X1),intersection(X0,intersection(X0,X1))) )
| ~ spl0_134
| ~ spl0_327 ),
inference(resolution,[],[f3211,f1084]) ).
fof(f24078,plain,
( spl0_1105
| ~ spl0_135
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f3378,f3210,f1087,f24076]) ).
fof(f24076,plain,
( spl0_1105
<=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,intersection(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f3378,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,intersection(X0,X1)))
| ~ spl0_135
| ~ spl0_327 ),
inference(duplicate_literal_removal,[],[f3347]) ).
fof(f3347,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),intersection(X1,intersection(X0,X1)))
| subclass(intersection(X0,X1),intersection(X1,intersection(X0,X1))) )
| ~ spl0_135
| ~ spl0_327 ),
inference(resolution,[],[f3211,f1088]) ).
fof(f24074,plain,
( spl0_1104
| ~ spl0_320
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f3373,f3210,f3172,f24072]) ).
fof(f24072,plain,
( spl0_1104
<=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,intersection(singleton_relation,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f3172,plain,
( spl0_320
<=> ! [X0,X1] :
( subclass(intersection(singleton_relation,X0),X1)
| member(not_subclass_element(intersection(singleton_relation,X0),X1),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f3373,plain,
( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,intersection(singleton_relation,X0)))
| ~ spl0_320
| ~ spl0_327 ),
inference(duplicate_literal_removal,[],[f3353]) ).
fof(f3353,plain,
( ! [X0] :
( subclass(intersection(singleton_relation,X0),intersection(element_relation,intersection(singleton_relation,X0)))
| subclass(intersection(singleton_relation,X0),intersection(element_relation,intersection(singleton_relation,X0))) )
| ~ spl0_320
| ~ spl0_327 ),
inference(resolution,[],[f3211,f3173]) ).
fof(f3173,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(singleton_relation,X0),X1),element_relation)
| subclass(intersection(singleton_relation,X0),X1) )
| ~ spl0_320 ),
inference(avatar_component_clause,[],[f3172]) ).
fof(f24070,plain,
( spl0_1103
| ~ spl0_324
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f3372,f3210,f3193,f24068]) ).
fof(f24068,plain,
( spl0_1103
<=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,intersection(X0,singleton_relation))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f3193,plain,
( spl0_324
<=> ! [X0,X1] :
( subclass(intersection(X0,singleton_relation),X1)
| member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f3372,plain,
( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,intersection(X0,singleton_relation)))
| ~ spl0_324
| ~ spl0_327 ),
inference(duplicate_literal_removal,[],[f3354]) ).
fof(f3354,plain,
( ! [X0] :
( subclass(intersection(X0,singleton_relation),intersection(element_relation,intersection(X0,singleton_relation)))
| subclass(intersection(X0,singleton_relation),intersection(element_relation,intersection(X0,singleton_relation))) )
| ~ spl0_324
| ~ spl0_327 ),
inference(resolution,[],[f3211,f3194]) ).
fof(f3194,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation)
| subclass(intersection(X0,singleton_relation),X1) )
| ~ spl0_324 ),
inference(avatar_component_clause,[],[f3193]) ).
fof(f24066,plain,
( ~ spl0_1101
| spl0_1102
| ~ spl0_13
| ~ spl0_1027 ),
inference(avatar_split_clause,[],[f21951,f21739,f258,f24063,f24059]) ).
fof(f24059,plain,
( spl0_1101
<=> inductive(complement(omega)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f24063,plain,
( spl0_1102
<=> null_class = omega ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f258,plain,
( spl0_13
<=> ! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f21739,plain,
( spl0_1027
<=> ! [X0] :
( null_class = X0
| ~ subclass(X0,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f21951,plain,
( null_class = omega
| ~ inductive(complement(omega))
| ~ spl0_13
| ~ spl0_1027 ),
inference(resolution,[],[f21740,f259]) ).
fof(f259,plain,
( ! [X1] :
( subclass(omega,X1)
| ~ inductive(X1) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f21740,plain,
( ! [X0] :
( ~ subclass(X0,complement(X0))
| null_class = X0 )
| ~ spl0_1027 ),
inference(avatar_component_clause,[],[f21739]) ).
fof(f24057,plain,
( ~ spl0_1100
| spl0_274
| ~ spl0_275
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f2970,f2818,f2539,f2535,f24054]) ).
fof(f24054,plain,
( spl0_1100
<=> subclass(subset_relation,complement(cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f2535,plain,
( spl0_274
<=> null_class = subset_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f2970,plain,
( null_class = subset_relation
| ~ subclass(subset_relation,complement(cross_product(universal_class,universal_class)))
| ~ spl0_275
| ~ spl0_292 ),
inference(resolution,[],[f2819,f2541]) ).
fof(f2541,plain,
( member(regular(subset_relation),cross_product(universal_class,universal_class))
| ~ spl0_275 ),
inference(avatar_component_clause,[],[f2539]) ).
fof(f24052,plain,
( spl0_1099
| ~ spl0_235
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f2881,f2529,f2310,f24050]) ).
fof(f24050,plain,
( spl0_1099
<=> ! [X0] :
( ~ member(X0,compose(element_relation,complement(singleton_relation)))
| ~ member(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f2529,plain,
( spl0_273
<=> ! [X0] :
( ~ member(X0,singleton_relation)
| ~ member(X0,compose(element_relation,complement(identity_relation))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f2881,plain,
( ! [X0] :
( ~ member(X0,compose(element_relation,complement(singleton_relation)))
| ~ member(X0,singleton_relation) )
| ~ spl0_235
| ~ spl0_273 ),
inference(superposition,[],[f2530,f2312]) ).
fof(f2530,plain,
( ! [X0] :
( ~ member(X0,compose(element_relation,complement(identity_relation)))
| ~ member(X0,singleton_relation) )
| ~ spl0_273 ),
inference(avatar_component_clause,[],[f2529]) ).
fof(f24048,plain,
( spl0_1098
| ~ spl0_41
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2865,f2310,f384,f24045]) ).
fof(f24045,plain,
( spl0_1098
<=> singleton_relation = intersection(complement(compose(element_relation,complement(singleton_relation))),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f2865,plain,
( singleton_relation = intersection(complement(compose(element_relation,complement(singleton_relation))),element_relation)
| ~ spl0_41
| ~ spl0_235 ),
inference(superposition,[],[f386,f2312]) ).
fof(f24043,plain,
( spl0_1097
| ~ spl0_38
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f2717,f2539,f372,f24041]) ).
fof(f24041,plain,
( spl0_1097
<=> ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(regular(subset_relation),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f2717,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(regular(subset_relation),X0) )
| ~ spl0_38
| ~ spl0_275 ),
inference(resolution,[],[f2541,f373]) ).
fof(f24039,plain,
( spl0_1096
| ~ spl0_110
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2245,f2227,f819,f24037]) ).
fof(f24037,plain,
( spl0_1096
<=> ! [X0] :
( omega = intersection(X0,omega)
| ~ inductive(intersection(X0,omega)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f819,plain,
( spl0_110
<=> ! [X0] :
( ~ subclass(X0,omega)
| omega = X0
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f2245,plain,
( ! [X0] :
( omega = intersection(X0,omega)
| ~ inductive(intersection(X0,omega)) )
| ~ spl0_110
| ~ spl0_224 ),
inference(resolution,[],[f2228,f820]) ).
fof(f820,plain,
( ! [X0] :
( ~ subclass(X0,omega)
| omega = X0
| ~ inductive(X0) )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f819]) ).
fof(f24035,plain,
( spl0_1095
| ~ spl0_110
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2234,f2223,f819,f24033]) ).
fof(f24033,plain,
( spl0_1095
<=> ! [X0] :
( omega = intersection(omega,X0)
| ~ inductive(intersection(omega,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f2234,plain,
( ! [X0] :
( omega = intersection(omega,X0)
| ~ inductive(intersection(omega,X0)) )
| ~ spl0_110
| ~ spl0_223 ),
inference(resolution,[],[f2224,f820]) ).
fof(f23186,plain,
( ~ spl0_1094
| spl0_813
| ~ spl0_1076 ),
inference(avatar_split_clause,[],[f23094,f22935,f15279,f23183]) ).
fof(f23183,plain,
( spl0_1094
<=> subclass(composition_function,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f15279,plain,
( spl0_813
<=> subclass(composition_function,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f22935,plain,
( spl0_1076
<=> ! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ subclass(X0,subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f23094,plain,
( ~ subclass(composition_function,subset_relation)
| spl0_813
| ~ spl0_1076 ),
inference(resolution,[],[f22936,f15281]) ).
fof(f15281,plain,
( ~ subclass(composition_function,cross_product(universal_class,universal_class))
| spl0_813 ),
inference(avatar_component_clause,[],[f15279]) ).
fof(f22936,plain,
( ! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ subclass(X0,subset_relation) )
| ~ spl0_1076 ),
inference(avatar_component_clause,[],[f22935]) ).
fof(f23027,plain,
( spl0_1093
| ~ spl0_268
| ~ spl0_681 ),
inference(avatar_split_clause,[],[f10727,f10597,f2499,f23025]) ).
fof(f23025,plain,
( spl0_1093
<=> ! [X0] :
( ~ subclass(universal_class,flip(X0))
| ~ subclass(universal_class,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f10727,plain,
( ! [X0] :
( ~ subclass(universal_class,flip(X0))
| ~ subclass(universal_class,complement(X0)) )
| ~ spl0_268
| ~ spl0_681 ),
inference(resolution,[],[f10598,f2500]) ).
fof(f23023,plain,
( spl0_1092
| ~ spl0_268
| ~ spl0_680 ),
inference(avatar_split_clause,[],[f10642,f10593,f2499,f23021]) ).
fof(f23021,plain,
( spl0_1092
<=> ! [X0] :
( ~ subclass(universal_class,rotate(X0))
| ~ subclass(universal_class,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f10642,plain,
( ! [X0] :
( ~ subclass(universal_class,rotate(X0))
| ~ subclass(universal_class,complement(X0)) )
| ~ spl0_268
| ~ spl0_680 ),
inference(resolution,[],[f10594,f2500]) ).
fof(f23019,plain,
( spl0_1091
| ~ spl0_235
| ~ spl0_244
| ~ spl0_397 ),
inference(avatar_split_clause,[],[f4731,f4270,f2364,f2310,f23017]) ).
fof(f23017,plain,
( spl0_1091
<=> ! [X0] :
( ~ subclass(singleton_relation,X0)
| subclass(singleton_relation,intersection(subset_relation,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f4731,plain,
( ! [X0] :
( ~ subclass(singleton_relation,X0)
| subclass(singleton_relation,intersection(subset_relation,X0)) )
| ~ spl0_235
| ~ spl0_244
| ~ spl0_397 ),
inference(forward_demodulation,[],[f4730,f2312]) ).
fof(f4730,plain,
( ! [X0] :
( subclass(singleton_relation,intersection(subset_relation,X0))
| ~ subclass(identity_relation,X0) )
| ~ spl0_235
| ~ spl0_244
| ~ spl0_397 ),
inference(forward_demodulation,[],[f4710,f2312]) ).
fof(f4710,plain,
( ! [X0] :
( subclass(identity_relation,intersection(subset_relation,X0))
| ~ subclass(identity_relation,X0) )
| ~ spl0_244
| ~ spl0_397 ),
inference(duplicate_literal_removal,[],[f4697]) ).
fof(f4697,plain,
( ! [X0] :
( subclass(identity_relation,intersection(subset_relation,X0))
| ~ subclass(identity_relation,X0)
| subclass(identity_relation,intersection(subset_relation,X0)) )
| ~ spl0_244
| ~ spl0_397 ),
inference(resolution,[],[f4271,f2365]) ).
fof(f23015,plain,
( spl0_1090
| ~ spl0_27
| ~ spl0_397 ),
inference(avatar_split_clause,[],[f4725,f4270,f319,f23013]) ).
fof(f23013,plain,
( spl0_1090
<=> ! [X0,X1] :
( subclass(X0,intersection(X0,X1))
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f4725,plain,
( ! [X0,X1] :
( subclass(X0,intersection(X0,X1))
| ~ subclass(X0,X1) )
| ~ spl0_27
| ~ spl0_397 ),
inference(duplicate_literal_removal,[],[f4673]) ).
fof(f4673,plain,
( ! [X0,X1] :
( subclass(X0,intersection(X0,X1))
| ~ subclass(X0,X1)
| subclass(X0,intersection(X0,X1)) )
| ~ spl0_27
| ~ spl0_397 ),
inference(resolution,[],[f4271,f320]) ).
fof(f23011,plain,
( spl0_1089
| ~ spl0_243
| ~ spl0_397 ),
inference(avatar_split_clause,[],[f4716,f4270,f2360,f23009]) ).
fof(f23009,plain,
( spl0_1089
<=> ! [X0] :
( subclass(singleton_relation,intersection(element_relation,X0))
| ~ subclass(singleton_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f4716,plain,
( ! [X0] :
( subclass(singleton_relation,intersection(element_relation,X0))
| ~ subclass(singleton_relation,X0) )
| ~ spl0_243
| ~ spl0_397 ),
inference(duplicate_literal_removal,[],[f4683]) ).
fof(f4683,plain,
( ! [X0] :
( subclass(singleton_relation,intersection(element_relation,X0))
| ~ subclass(singleton_relation,X0)
| subclass(singleton_relation,intersection(element_relation,X0)) )
| ~ spl0_243
| ~ spl0_397 ),
inference(resolution,[],[f4271,f2361]) ).
fof(f22996,plain,
( spl0_1088
| ~ spl0_28
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f4635,f4239,f323,f22994]) ).
fof(f22994,plain,
( spl0_1088
<=> ! [X0,X1] :
( subclass(intersection(X0,null_class),X1)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f323,plain,
( spl0_28
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f4635,plain,
( ! [X0,X1] :
( subclass(intersection(X0,null_class),X1)
| null_class = X1 )
| ~ spl0_28
| ~ spl0_391 ),
inference(duplicate_literal_removal,[],[f4597]) ).
fof(f4597,plain,
( ! [X0,X1] :
( subclass(intersection(X0,null_class),X1)
| null_class = X1
| subclass(intersection(X0,null_class),X1) )
| ~ spl0_28
| ~ spl0_391 ),
inference(resolution,[],[f4240,f324]) ).
fof(f324,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f22992,plain,
( spl0_1087
| ~ spl0_28
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f4592,f4235,f323,f22990]) ).
fof(f4592,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| subclass(intersection(X2,X0),X1) )
| ~ spl0_28
| ~ spl0_390 ),
inference(duplicate_literal_removal,[],[f4547]) ).
fof(f4547,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| subclass(intersection(X2,X0),X1)
| subclass(intersection(X2,X0),X1) )
| ~ spl0_28
| ~ spl0_390 ),
inference(resolution,[],[f4236,f324]) ).
fof(f22987,plain,
( spl0_1086
| ~ spl0_28
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f4542,f4231,f323,f22985]) ).
fof(f22985,plain,
( spl0_1086
<=> ! [X0,X1] :
( subclass(intersection(null_class,X0),X1)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f4542,plain,
( ! [X0,X1] :
( subclass(intersection(null_class,X0),X1)
| null_class = X1 )
| ~ spl0_28
| ~ spl0_389 ),
inference(duplicate_literal_removal,[],[f4504]) ).
fof(f4504,plain,
( ! [X0,X1] :
( subclass(intersection(null_class,X0),X1)
| null_class = X1
| subclass(intersection(null_class,X0),X1) )
| ~ spl0_28
| ~ spl0_389 ),
inference(resolution,[],[f4232,f324]) ).
fof(f22983,plain,
( spl0_1085
| ~ spl0_28
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f4496,f4227,f323,f22981]) ).
fof(f22981,plain,
( spl0_1085
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| subclass(intersection(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f4496,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| subclass(intersection(X0,X2),X1) )
| ~ spl0_28
| ~ spl0_388 ),
inference(duplicate_literal_removal,[],[f4451]) ).
fof(f4451,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| subclass(intersection(X0,X2),X1)
| subclass(intersection(X0,X2),X1) )
| ~ spl0_28
| ~ spl0_388 ),
inference(resolution,[],[f4228,f324]) ).
fof(f22979,plain,
( spl0_1084
| ~ spl0_351
| ~ spl0_387 ),
inference(avatar_split_clause,[],[f4439,f4223,f3525,f22977]) ).
fof(f22977,plain,
( spl0_1084
<=> ! [X0,X1] : null_class = intersection(complement(X0),intersection(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f4223,plain,
( spl0_387
<=> ! [X2,X0,X1] :
( null_class = intersection(X0,intersection(X1,X2))
| member(regular(intersection(X0,intersection(X1,X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f4439,plain,
( ! [X0,X1] : null_class = intersection(complement(X0),intersection(X0,X1))
| ~ spl0_351
| ~ spl0_387 ),
inference(duplicate_literal_removal,[],[f4409]) ).
fof(f4409,plain,
( ! [X0,X1] :
( null_class = intersection(complement(X0),intersection(X0,X1))
| null_class = intersection(complement(X0),intersection(X0,X1)) )
| ~ spl0_351
| ~ spl0_387 ),
inference(resolution,[],[f4224,f3526]) ).
fof(f4224,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(X0,intersection(X1,X2))),X1)
| null_class = intersection(X0,intersection(X1,X2)) )
| ~ spl0_387 ),
inference(avatar_component_clause,[],[f4223]) ).
fof(f22975,plain,
( spl0_1083
| ~ spl0_351
| ~ spl0_386 ),
inference(avatar_split_clause,[],[f4398,f4219,f3525,f22973]) ).
fof(f22973,plain,
( spl0_1083
<=> ! [X0,X1] : null_class = intersection(complement(X0),intersection(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f4219,plain,
( spl0_386
<=> ! [X2,X0,X1] :
( null_class = intersection(X0,intersection(X1,X2))
| member(regular(intersection(X0,intersection(X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f4398,plain,
( ! [X0,X1] : null_class = intersection(complement(X0),intersection(X1,X0))
| ~ spl0_351
| ~ spl0_386 ),
inference(duplicate_literal_removal,[],[f4368]) ).
fof(f4368,plain,
( ! [X0,X1] :
( null_class = intersection(complement(X0),intersection(X1,X0))
| null_class = intersection(complement(X0),intersection(X1,X0)) )
| ~ spl0_351
| ~ spl0_386 ),
inference(resolution,[],[f4220,f3526]) ).
fof(f4220,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(X0,intersection(X1,X2))),X2)
| null_class = intersection(X0,intersection(X1,X2)) )
| ~ spl0_386 ),
inference(avatar_component_clause,[],[f4219]) ).
fof(f22971,plain,
( spl0_1082
| ~ spl0_352
| ~ spl0_385 ),
inference(avatar_split_clause,[],[f4351,f4215,f3529,f22969]) ).
fof(f22969,plain,
( spl0_1082
<=> ! [X0,X1] : null_class = intersection(intersection(X0,X1),complement(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f4215,plain,
( spl0_385
<=> ! [X2,X0,X1] :
( null_class = intersection(intersection(X0,X1),X2)
| member(regular(intersection(intersection(X0,X1),X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f4351,plain,
( ! [X0,X1] : null_class = intersection(intersection(X0,X1),complement(X0))
| ~ spl0_352
| ~ spl0_385 ),
inference(duplicate_literal_removal,[],[f4321]) ).
fof(f4321,plain,
( ! [X0,X1] :
( null_class = intersection(intersection(X0,X1),complement(X0))
| null_class = intersection(intersection(X0,X1),complement(X0)) )
| ~ spl0_352
| ~ spl0_385 ),
inference(resolution,[],[f4216,f3530]) ).
fof(f4216,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(intersection(X0,X1),X2)),X0)
| null_class = intersection(intersection(X0,X1),X2) )
| ~ spl0_385 ),
inference(avatar_component_clause,[],[f4215]) ).
fof(f22967,plain,
( spl0_1081
| ~ spl0_352
| ~ spl0_384 ),
inference(avatar_split_clause,[],[f4312,f4211,f3529,f22965]) ).
fof(f22965,plain,
( spl0_1081
<=> ! [X0,X1] : null_class = intersection(intersection(X0,X1),complement(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f4211,plain,
( spl0_384
<=> ! [X2,X0,X1] :
( null_class = intersection(intersection(X0,X1),X2)
| member(regular(intersection(intersection(X0,X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f4312,plain,
( ! [X0,X1] : null_class = intersection(intersection(X0,X1),complement(X1))
| ~ spl0_352
| ~ spl0_384 ),
inference(duplicate_literal_removal,[],[f4282]) ).
fof(f4282,plain,
( ! [X0,X1] :
( null_class = intersection(intersection(X0,X1),complement(X1))
| null_class = intersection(intersection(X0,X1),complement(X1)) )
| ~ spl0_352
| ~ spl0_384 ),
inference(resolution,[],[f4212,f3530]) ).
fof(f4212,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(intersection(X0,X1),X2)),X1)
| null_class = intersection(intersection(X0,X1),X2) )
| ~ spl0_384 ),
inference(avatar_component_clause,[],[f4211]) ).
fof(f22963,plain,
( spl0_1080
| ~ spl0_130
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f3377,f3210,f1012,f22961]) ).
fof(f22961,plain,
( spl0_1080
<=> ! [X0,X1] :
( subclass(X0,intersection(X1,X0))
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f3377,plain,
( ! [X0,X1] :
( subclass(X0,intersection(X1,X0))
| ~ subclass(X0,X1) )
| ~ spl0_130
| ~ spl0_327 ),
inference(duplicate_literal_removal,[],[f3348]) ).
fof(f3348,plain,
( ! [X0,X1] :
( subclass(X0,intersection(X1,X0))
| ~ subclass(X0,X1)
| subclass(X0,intersection(X1,X0)) )
| ~ spl0_130
| ~ spl0_327 ),
inference(resolution,[],[f3211,f1013]) ).
fof(f22959,plain,
( spl0_1079
| ~ spl0_302
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f3374,f3210,f2940,f22957]) ).
fof(f22957,plain,
( spl0_1079
<=> ! [X0] :
( subclass(X0,intersection(element_relation,X0))
| ~ subclass(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f3374,plain,
( ! [X0] :
( subclass(X0,intersection(element_relation,X0))
| ~ subclass(X0,singleton_relation) )
| ~ spl0_302
| ~ spl0_327 ),
inference(duplicate_literal_removal,[],[f3352]) ).
fof(f3352,plain,
( ! [X0] :
( subclass(X0,intersection(element_relation,X0))
| subclass(X0,intersection(element_relation,X0))
| ~ subclass(X0,singleton_relation) )
| ~ spl0_302
| ~ spl0_327 ),
inference(resolution,[],[f3211,f2941]) ).
fof(f22945,plain,
( spl0_1078
| ~ spl0_310
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f3370,f3210,f3092,f22943]) ).
fof(f22943,plain,
( spl0_1078
<=> ! [X0] :
( subclass(X0,intersection(subset_relation,X0))
| ~ subclass(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f3370,plain,
( ! [X0] :
( subclass(X0,intersection(subset_relation,X0))
| ~ subclass(X0,singleton_relation) )
| ~ spl0_310
| ~ spl0_327 ),
inference(duplicate_literal_removal,[],[f3363]) ).
fof(f3363,plain,
( ! [X0] :
( subclass(X0,intersection(subset_relation,X0))
| subclass(X0,intersection(subset_relation,X0))
| ~ subclass(X0,singleton_relation) )
| ~ spl0_310
| ~ spl0_327 ),
inference(resolution,[],[f3211,f3093]) ).
fof(f22941,plain,
( spl0_1077
| ~ spl0_310
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3235,f3137,f3092,f22939]) ).
fof(f22939,plain,
( spl0_1077
<=> ! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ subclass(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f3235,plain,
( ! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ subclass(X0,singleton_relation) )
| ~ spl0_310
| ~ spl0_313 ),
inference(duplicate_literal_removal,[],[f3226]) ).
fof(f3226,plain,
( ! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| subclass(X0,cross_product(universal_class,universal_class))
| ~ subclass(X0,singleton_relation) )
| ~ spl0_310
| ~ spl0_313 ),
inference(resolution,[],[f3138,f3093]) ).
fof(f22937,plain,
( spl0_1076
| ~ spl0_130
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3231,f3137,f1012,f22935]) ).
fof(f3231,plain,
( ! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ subclass(X0,subset_relation) )
| ~ spl0_130
| ~ spl0_313 ),
inference(duplicate_literal_removal,[],[f3230]) ).
fof(f3230,plain,
( ! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ subclass(X0,subset_relation)
| subclass(X0,cross_product(universal_class,universal_class)) )
| ~ spl0_130
| ~ spl0_313 ),
inference(resolution,[],[f3138,f1013]) ).
fof(f22924,plain,
( ~ spl0_350
| spl0_1075
| ~ spl0_144
| ~ spl0_235
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f3084,f3070,f2310,f1167,f22921,f3520]) ).
fof(f3520,plain,
( spl0_350
<=> member(regular(singleton_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f22921,plain,
( spl0_1075
<=> member(regular(singleton_relation),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f1167,plain,
( spl0_144
<=> ! [X0] :
( member(X0,identity_relation)
| ~ member(X0,subset_relation)
| ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f3070,plain,
( spl0_309
<=> member(regular(singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f3084,plain,
( member(regular(singleton_relation),singleton_relation)
| ~ member(regular(singleton_relation),subset_relation)
| ~ spl0_144
| ~ spl0_235
| ~ spl0_309 ),
inference(forward_demodulation,[],[f3080,f2312]) ).
fof(f3080,plain,
( ~ member(regular(singleton_relation),subset_relation)
| member(regular(singleton_relation),identity_relation)
| ~ spl0_144
| ~ spl0_309 ),
inference(resolution,[],[f3072,f1168]) ).
fof(f1168,plain,
( ! [X0] :
( ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,subset_relation)
| member(X0,identity_relation) )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1167]) ).
fof(f3072,plain,
( member(regular(singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_309 ),
inference(avatar_component_clause,[],[f3070]) ).
fof(f22919,plain,
( spl0_1074
| ~ spl0_37
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f2921,f2503,f359,f22917]) ).
fof(f22917,plain,
( spl0_1074
<=> ! [X0] :
( ~ inductive(domain_of(flip(cross_product(X0,universal_class))))
| ~ one_to_one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f359,plain,
( spl0_37
<=> ! [X8] :
( ~ one_to_one(X8)
| function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f2503,plain,
( spl0_269
<=> ! [X0] :
( ~ inductive(X0)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f2921,plain,
( ! [X0] :
( ~ inductive(domain_of(flip(cross_product(X0,universal_class))))
| ~ one_to_one(X0) )
| ~ spl0_37
| ~ spl0_269 ),
inference(resolution,[],[f2504,f360]) ).
fof(f360,plain,
( ! [X8] :
( function(domain_of(flip(cross_product(X8,universal_class))))
| ~ one_to_one(X8) )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f2504,plain,
( ! [X0] :
( ~ function(X0)
| ~ inductive(X0) )
| ~ spl0_269 ),
inference(avatar_component_clause,[],[f2503]) ).
fof(f22915,plain,
( spl0_1073
| ~ spl0_235
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f2877,f2364,f2310,f22913]) ).
fof(f22913,plain,
( spl0_1073
<=> ! [X0] :
( member(not_subclass_element(singleton_relation,X0),subset_relation)
| subclass(singleton_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f2877,plain,
( ! [X0] :
( member(not_subclass_element(singleton_relation,X0),subset_relation)
| subclass(singleton_relation,X0) )
| ~ spl0_235
| ~ spl0_244 ),
inference(superposition,[],[f2365,f2312]) ).
fof(f22911,plain,
( ~ spl0_1071
| spl0_1072
| ~ spl0_112
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f2779,f2731,f884,f22908,f22904]) ).
fof(f22904,plain,
( spl0_1071
<=> subclass(complement(element_relation),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f22908,plain,
( spl0_1072
<=> null_class = complement(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f884,plain,
( spl0_112
<=> ! [X0] :
( complement(X0) = null_class
| ~ member(regular(complement(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f2779,plain,
( null_class = complement(element_relation)
| ~ subclass(complement(element_relation),singleton_relation)
| ~ spl0_112
| ~ spl0_285 ),
inference(duplicate_literal_removal,[],[f2771]) ).
fof(f2771,plain,
( null_class = complement(element_relation)
| ~ subclass(complement(element_relation),singleton_relation)
| null_class = complement(element_relation)
| ~ spl0_112
| ~ spl0_285 ),
inference(resolution,[],[f2732,f885]) ).
fof(f885,plain,
( ! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f884]) ).
fof(f22902,plain,
( spl0_1070
| ~ spl0_43
| ~ spl0_235
| ~ spl0_1047 ),
inference(avatar_split_clause,[],[f22501,f21824,f2310,f393,f22899]) ).
fof(f22899,plain,
( spl0_1070
<=> subclass(singleton_relation,intersection(subset_relation,subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f21824,plain,
( spl0_1047
<=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f22501,plain,
( subclass(singleton_relation,intersection(subset_relation,subset_relation))
| ~ spl0_43
| ~ spl0_235
| ~ spl0_1047 ),
inference(forward_demodulation,[],[f22495,f2312]) ).
fof(f22495,plain,
( subclass(identity_relation,intersection(subset_relation,subset_relation))
| ~ spl0_43
| ~ spl0_1047 ),
inference(superposition,[],[f21825,f395]) ).
fof(f21825,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X1))
| ~ spl0_1047 ),
inference(avatar_component_clause,[],[f21824]) ).
fof(f22897,plain,
( ~ spl0_1069
| ~ spl0_235
| spl0_1067 ),
inference(avatar_split_clause,[],[f22892,f22884,f2310,f22894]) ).
fof(f22894,plain,
( spl0_1069
<=> subclass(complement(subset_relation),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f22884,plain,
( spl0_1067
<=> subclass(complement(subset_relation),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f22892,plain,
( ~ subclass(complement(subset_relation),singleton_relation)
| ~ spl0_235
| spl0_1067 ),
inference(forward_demodulation,[],[f22886,f2312]) ).
fof(f22886,plain,
( ~ subclass(complement(subset_relation),identity_relation)
| spl0_1067 ),
inference(avatar_component_clause,[],[f22884]) ).
fof(f22891,plain,
( ~ spl0_1067
| spl0_1068
| ~ spl0_112
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f2770,f2723,f884,f22888,f22884]) ).
fof(f22888,plain,
( spl0_1068
<=> null_class = complement(subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f2770,plain,
( null_class = complement(subset_relation)
| ~ subclass(complement(subset_relation),identity_relation)
| ~ spl0_112
| ~ spl0_283 ),
inference(duplicate_literal_removal,[],[f2762]) ).
fof(f2762,plain,
( null_class = complement(subset_relation)
| ~ subclass(complement(subset_relation),identity_relation)
| null_class = complement(subset_relation)
| ~ spl0_112
| ~ spl0_283 ),
inference(resolution,[],[f2724,f885]) ).
fof(f22770,plain,
( ~ spl0_275
| ~ spl0_1066 ),
inference(avatar_contradiction_clause,[],[f22754]) ).
fof(f22754,plain,
( $false
| ~ spl0_275
| ~ spl0_1066 ),
inference(resolution,[],[f22746,f2541]) ).
fof(f22746,plain,
( ! [X0] : ~ member(regular(subset_relation),X0)
| ~ spl0_1066 ),
inference(avatar_component_clause,[],[f22745]) ).
fof(f22745,plain,
( spl0_1066
<=> ! [X0] : ~ member(regular(subset_relation),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f22769,plain,
( ~ spl0_470
| ~ spl0_1066 ),
inference(avatar_contradiction_clause,[],[f22757]) ).
fof(f22757,plain,
( $false
| ~ spl0_470
| ~ spl0_1066 ),
inference(resolution,[],[f22746,f6193]) ).
fof(f22747,plain,
( spl0_1065
| spl0_1066
| ~ spl0_275
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f2715,f2558,f2539,f22745,f22741]) ).
fof(f22741,plain,
( spl0_1065
<=> member(regular(subset_relation),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f2558,plain,
( spl0_276
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f2715,plain,
( ! [X0] :
( ~ member(regular(subset_relation),X0)
| member(regular(subset_relation),universal_class) )
| ~ spl0_275
| ~ spl0_276 ),
inference(resolution,[],[f2541,f2559]) ).
fof(f2559,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,universal_class) )
| ~ spl0_276 ),
inference(avatar_component_clause,[],[f2558]) ).
fof(f22738,plain,
( spl0_1063
| spl0_1064
| ~ spl0_234
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f2671,f2558,f2304,f22736,f22732]) ).
fof(f22732,plain,
( spl0_1063
<=> member(regular(identity_relation),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f22736,plain,
( spl0_1064
<=> ! [X0] : ~ member(regular(identity_relation),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f2304,plain,
( spl0_234
<=> member(regular(identity_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f2671,plain,
( ! [X0] :
( ~ member(regular(identity_relation),X0)
| member(regular(identity_relation),universal_class) )
| ~ spl0_234
| ~ spl0_276 ),
inference(resolution,[],[f2559,f2306]) ).
fof(f2306,plain,
( member(regular(identity_relation),subset_relation)
| ~ spl0_234 ),
inference(avatar_component_clause,[],[f2304]) ).
fof(f22713,plain,
( spl0_1062
| ~ spl0_41
| ~ spl0_1047 ),
inference(avatar_split_clause,[],[f22490,f21824,f384,f22710]) ).
fof(f22710,plain,
( spl0_1062
<=> subclass(singleton_relation,intersection(element_relation,element_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f22490,plain,
( subclass(singleton_relation,intersection(element_relation,element_relation))
| ~ spl0_41
| ~ spl0_1047 ),
inference(superposition,[],[f21825,f386]) ).
fof(f22077,plain,
( ~ spl0_1061
| ~ spl0_926
| ~ spl0_1022 ),
inference(avatar_split_clause,[],[f21914,f21716,f18165,f22074]) ).
fof(f22074,plain,
( spl0_1061
<=> subclass(element_relation,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f18165,plain,
( spl0_926
<=> ! [X0] : ~ member(X0,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f21914,plain,
( ~ subclass(element_relation,null_class)
| ~ spl0_926
| ~ spl0_1022 ),
inference(resolution,[],[f21717,f18166]) ).
fof(f18166,plain,
( ! [X0] : ~ member(X0,null_class)
| ~ spl0_926 ),
inference(avatar_component_clause,[],[f18165]) ).
fof(f21884,plain,
( spl0_1060
| ~ spl0_50
| ~ spl0_786 ),
inference(avatar_split_clause,[],[f14742,f14703,f452,f21882]) ).
fof(f21882,plain,
( spl0_1060
<=> ! [X0] : intersection(null_class,X0) = intersection(X0,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f452,plain,
( spl0_50
<=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f14703,plain,
( spl0_786
<=> null_class = cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f14742,plain,
( ! [X0] : intersection(null_class,X0) = intersection(X0,null_class)
| ~ spl0_50
| ~ spl0_786 ),
inference(superposition,[],[f453,f14705]) ).
fof(f14705,plain,
( null_class = cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
| ~ spl0_786 ),
inference(avatar_component_clause,[],[f14703]) ).
fof(f453,plain,
( ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f21880,plain,
( spl0_1059
| ~ spl0_9
| ~ spl0_686 ),
inference(avatar_split_clause,[],[f10976,f10792,f240,f21877]) ).
fof(f21877,plain,
( spl0_1059
<=> member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f10976,plain,
( member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),universal_class)
| ~ spl0_9
| ~ spl0_686 ),
inference(superposition,[],[f241,f10794]) ).
fof(f21875,plain,
( spl0_1058
| ~ spl0_9
| ~ spl0_684 ),
inference(avatar_split_clause,[],[f10902,f10782,f240,f21872]) ).
fof(f21872,plain,
( spl0_1058
<=> member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f10902,plain,
( member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),universal_class)
| ~ spl0_9
| ~ spl0_684 ),
inference(superposition,[],[f241,f10784]) ).
fof(f21870,plain,
( spl0_1057
| ~ spl0_9
| ~ spl0_683 ),
inference(avatar_split_clause,[],[f10828,f10777,f240,f21867]) ).
fof(f21867,plain,
( spl0_1057
<=> member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f10828,plain,
( member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),universal_class)
| ~ spl0_9
| ~ spl0_683 ),
inference(superposition,[],[f241,f10779]) ).
fof(f21865,plain,
( spl0_642
| ~ spl0_1056
| ~ spl0_361
| ~ spl0_681 ),
inference(avatar_split_clause,[],[f10708,f10597,f3757,f21862,f9714]) ).
fof(f9714,plain,
( spl0_642
<=> ! [X0] : member(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f21862,plain,
( spl0_1056
<=> subclass(universal_class,flip(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f3757,plain,
( spl0_361
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f10708,plain,
( ! [X0] :
( ~ subclass(universal_class,flip(subset_relation))
| member(X0,universal_class) )
| ~ spl0_361
| ~ spl0_681 ),
inference(resolution,[],[f10598,f3758]) ).
fof(f3758,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(X1,universal_class) )
| ~ spl0_361 ),
inference(avatar_component_clause,[],[f3757]) ).
fof(f21860,plain,
( spl0_642
| ~ spl0_1055
| ~ spl0_361
| ~ spl0_680 ),
inference(avatar_split_clause,[],[f10623,f10593,f3757,f21857,f9714]) ).
fof(f21857,plain,
( spl0_1055
<=> subclass(universal_class,rotate(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f10623,plain,
( ! [X0] :
( ~ subclass(universal_class,rotate(subset_relation))
| member(X0,universal_class) )
| ~ spl0_361
| ~ spl0_680 ),
inference(resolution,[],[f10594,f3758]) ).
fof(f21855,plain,
( ~ spl0_1054
| spl0_652
| ~ spl0_66
| ~ spl0_489 ),
inference(avatar_split_clause,[],[f6764,f6441,f552,f9911,f21852]) ).
fof(f21852,plain,
( spl0_1054
<=> subclass(domain_relation,complement(domain_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f552,plain,
( spl0_66
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f6764,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| ~ subclass(domain_relation,complement(domain_relation)) )
| ~ spl0_66
| ~ spl0_489 ),
inference(duplicate_literal_removal,[],[f6763]) ).
fof(f6763,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| ~ subclass(domain_relation,complement(domain_relation))
| ~ member(X0,universal_class) )
| ~ spl0_66
| ~ spl0_489 ),
inference(resolution,[],[f6442,f553]) ).
fof(f553,plain,
( ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation)
| ~ member(X0,universal_class) )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f21850,plain,
( spl0_1053
| ~ spl0_134
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f5306,f4832,f1083,f21848]) ).
fof(f21848,plain,
( spl0_1053
<=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f5306,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X0,X0))
| ~ spl0_134
| ~ spl0_417 ),
inference(duplicate_literal_removal,[],[f5249]) ).
fof(f5249,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),intersection(X0,X0))
| subclass(intersection(X0,X1),intersection(X0,X0)) )
| ~ spl0_134
| ~ spl0_417 ),
inference(resolution,[],[f4833,f1084]) ).
fof(f21846,plain,
( spl0_1052
| ~ spl0_135
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f5303,f4832,f1087,f21844]) ).
fof(f21844,plain,
( spl0_1052
<=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f5303,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X0))
| ~ spl0_135
| ~ spl0_417 ),
inference(duplicate_literal_removal,[],[f5252]) ).
fof(f5252,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),intersection(X1,X0))
| subclass(intersection(X0,X1),intersection(X1,X0)) )
| ~ spl0_135
| ~ spl0_417 ),
inference(resolution,[],[f4833,f1088]) ).
fof(f21842,plain,
( spl0_1051
| ~ spl0_320
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f5294,f4832,f3172,f21840]) ).
fof(f21840,plain,
( spl0_1051
<=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,singleton_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f5294,plain,
( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,singleton_relation))
| ~ spl0_320
| ~ spl0_417 ),
inference(duplicate_literal_removal,[],[f5262]) ).
fof(f5262,plain,
( ! [X0] :
( subclass(intersection(singleton_relation,X0),intersection(element_relation,singleton_relation))
| subclass(intersection(singleton_relation,X0),intersection(element_relation,singleton_relation)) )
| ~ spl0_320
| ~ spl0_417 ),
inference(resolution,[],[f4833,f3173]) ).
fof(f21838,plain,
( spl0_1050
| ~ spl0_324
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f5293,f4832,f3193,f21836]) ).
fof(f21836,plain,
( spl0_1050
<=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f5293,plain,
( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,X0))
| ~ spl0_324
| ~ spl0_417 ),
inference(duplicate_literal_removal,[],[f5263]) ).
fof(f5263,plain,
( ! [X0] :
( subclass(intersection(X0,singleton_relation),intersection(element_relation,X0))
| subclass(intersection(X0,singleton_relation),intersection(element_relation,X0)) )
| ~ spl0_324
| ~ spl0_417 ),
inference(resolution,[],[f4833,f3194]) ).
fof(f21834,plain,
( spl0_1049
| ~ spl0_332
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f5291,f4832,f3310,f21832]) ).
fof(f21832,plain,
( spl0_1049
<=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,singleton_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f5291,plain,
( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,singleton_relation))
| ~ spl0_332
| ~ spl0_417 ),
inference(duplicate_literal_removal,[],[f5274]) ).
fof(f5274,plain,
( ! [X0] :
( subclass(intersection(singleton_relation,X0),intersection(subset_relation,singleton_relation))
| subclass(intersection(singleton_relation,X0),intersection(subset_relation,singleton_relation)) )
| ~ spl0_332
| ~ spl0_417 ),
inference(resolution,[],[f4833,f3311]) ).
fof(f21830,plain,
( spl0_1048
| ~ spl0_335
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f5290,f4832,f3332,f21828]) ).
fof(f21828,plain,
( spl0_1048
<=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f5290,plain,
( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,X0))
| ~ spl0_335
| ~ spl0_417 ),
inference(duplicate_literal_removal,[],[f5275]) ).
fof(f5275,plain,
( ! [X0] :
( subclass(intersection(X0,singleton_relation),intersection(subset_relation,X0))
| subclass(intersection(X0,singleton_relation),intersection(subset_relation,X0)) )
| ~ spl0_335
| ~ spl0_417 ),
inference(resolution,[],[f4833,f3333]) ).
fof(f21826,plain,
( spl0_1047
| ~ spl0_135
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f5238,f4828,f1087,f21824]) ).
fof(f5238,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X1))
| ~ spl0_135
| ~ spl0_416 ),
inference(duplicate_literal_removal,[],[f5187]) ).
fof(f5187,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),intersection(X1,X1))
| subclass(intersection(X0,X1),intersection(X1,X1)) )
| ~ spl0_135
| ~ spl0_416 ),
inference(resolution,[],[f4829,f1088]) ).
fof(f21822,plain,
( spl0_1046
| ~ spl0_320
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f5229,f4828,f3172,f21820]) ).
fof(f21820,plain,
( spl0_1046
<=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f5229,plain,
( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,X0))
| ~ spl0_320
| ~ spl0_416 ),
inference(duplicate_literal_removal,[],[f5197]) ).
fof(f5197,plain,
( ! [X0] :
( subclass(intersection(singleton_relation,X0),intersection(element_relation,X0))
| subclass(intersection(singleton_relation,X0),intersection(element_relation,X0)) )
| ~ spl0_320
| ~ spl0_416 ),
inference(resolution,[],[f4829,f3173]) ).
fof(f21818,plain,
( spl0_1045
| ~ spl0_324
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f5228,f4828,f3193,f21816]) ).
fof(f21816,plain,
( spl0_1045
<=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,singleton_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f5228,plain,
( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,singleton_relation))
| ~ spl0_324
| ~ spl0_416 ),
inference(duplicate_literal_removal,[],[f5198]) ).
fof(f5198,plain,
( ! [X0] :
( subclass(intersection(X0,singleton_relation),intersection(element_relation,singleton_relation))
| subclass(intersection(X0,singleton_relation),intersection(element_relation,singleton_relation)) )
| ~ spl0_324
| ~ spl0_416 ),
inference(resolution,[],[f4829,f3194]) ).
fof(f21814,plain,
( spl0_1044
| ~ spl0_332
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f5226,f4828,f3310,f21812]) ).
fof(f21812,plain,
( spl0_1044
<=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f5226,plain,
( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,X0))
| ~ spl0_332
| ~ spl0_416 ),
inference(duplicate_literal_removal,[],[f5209]) ).
fof(f5209,plain,
( ! [X0] :
( subclass(intersection(singleton_relation,X0),intersection(subset_relation,X0))
| subclass(intersection(singleton_relation,X0),intersection(subset_relation,X0)) )
| ~ spl0_332
| ~ spl0_416 ),
inference(resolution,[],[f4829,f3311]) ).
fof(f21810,plain,
( spl0_1043
| ~ spl0_335
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f5225,f4828,f3332,f21808]) ).
fof(f21808,plain,
( spl0_1043
<=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,singleton_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f5225,plain,
( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,singleton_relation))
| ~ spl0_335
| ~ spl0_416 ),
inference(duplicate_literal_removal,[],[f5210]) ).
fof(f5210,plain,
( ! [X0] :
( subclass(intersection(X0,singleton_relation),intersection(subset_relation,singleton_relation))
| subclass(intersection(X0,singleton_relation),intersection(subset_relation,singleton_relation)) )
| ~ spl0_335
| ~ spl0_416 ),
inference(resolution,[],[f4829,f3333]) ).
fof(f21806,plain,
( spl0_1042
| ~ spl0_28
| ~ spl0_407 ),
inference(avatar_split_clause,[],[f5078,f4790,f323,f21804]) ).
fof(f21804,plain,
( spl0_1042
<=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f5078,plain,
( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),X1)
| ~ spl0_28
| ~ spl0_407 ),
inference(duplicate_literal_removal,[],[f5032]) ).
fof(f5032,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,intersection(X1,X2)),X1)
| subclass(intersection(X0,intersection(X1,X2)),X1) )
| ~ spl0_28
| ~ spl0_407 ),
inference(resolution,[],[f4791,f324]) ).
fof(f21802,plain,
( spl0_1041
| ~ spl0_28
| ~ spl0_406 ),
inference(avatar_split_clause,[],[f5020,f4786,f323,f21800]) ).
fof(f21800,plain,
( spl0_1041
<=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f5020,plain,
( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),X2)
| ~ spl0_28
| ~ spl0_406 ),
inference(duplicate_literal_removal,[],[f4974]) ).
fof(f4974,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,intersection(X1,X2)),X2)
| subclass(intersection(X0,intersection(X1,X2)),X2) )
| ~ spl0_28
| ~ spl0_406 ),
inference(resolution,[],[f4787,f324]) ).
fof(f21798,plain,
( spl0_1040
| ~ spl0_28
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f4961,f4782,f323,f21796]) ).
fof(f21796,plain,
( spl0_1040
<=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f4961,plain,
( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),X0)
| ~ spl0_28
| ~ spl0_405 ),
inference(duplicate_literal_removal,[],[f4915]) ).
fof(f4915,plain,
( ! [X2,X0,X1] :
( subclass(intersection(intersection(X0,X1),X2),X0)
| subclass(intersection(intersection(X0,X1),X2),X0) )
| ~ spl0_28
| ~ spl0_405 ),
inference(resolution,[],[f4783,f324]) ).
fof(f21794,plain,
( spl0_1039
| ~ spl0_28
| ~ spl0_404 ),
inference(avatar_split_clause,[],[f4903,f4778,f323,f21792]) ).
fof(f21792,plain,
( spl0_1039
<=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f4903,plain,
( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),X1)
| ~ spl0_28
| ~ spl0_404 ),
inference(duplicate_literal_removal,[],[f4857]) ).
fof(f4857,plain,
( ! [X2,X0,X1] :
( subclass(intersection(intersection(X0,X1),X2),X1)
| subclass(intersection(intersection(X0,X1),X2),X1) )
| ~ spl0_28
| ~ spl0_404 ),
inference(resolution,[],[f4779,f324]) ).
fof(f21790,plain,
( spl0_1038
| ~ spl0_313
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f3450,f3332,f3137,f21788]) ).
fof(f21788,plain,
( spl0_1038
<=> ! [X0] : subclass(intersection(X0,singleton_relation),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f3450,plain,
( ! [X0] : subclass(intersection(X0,singleton_relation),cross_product(universal_class,universal_class))
| ~ spl0_313
| ~ spl0_335 ),
inference(duplicate_literal_removal,[],[f3441]) ).
fof(f3441,plain,
( ! [X0] :
( subclass(intersection(X0,singleton_relation),cross_product(universal_class,universal_class))
| subclass(intersection(X0,singleton_relation),cross_product(universal_class,universal_class)) )
| ~ spl0_313
| ~ spl0_335 ),
inference(resolution,[],[f3333,f3138]) ).
fof(f21786,plain,
( spl0_1037
| ~ spl0_28
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f3437,f3328,f323,f21783]) ).
fof(f21783,plain,
( spl0_1037
<=> subclass(singleton_relation,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f3437,plain,
( subclass(singleton_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_28
| ~ spl0_334 ),
inference(duplicate_literal_removal,[],[f3426]) ).
fof(f3426,plain,
( subclass(singleton_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(singleton_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_28
| ~ spl0_334 ),
inference(resolution,[],[f3329,f324]) ).
fof(f21781,plain,
( spl0_1036
| ~ spl0_28
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f3425,f3324,f323,f21778]) ).
fof(f21778,plain,
( spl0_1036
<=> subclass(singleton_relation,complement(compose(element_relation,complement(singleton_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f3425,plain,
( subclass(singleton_relation,complement(compose(element_relation,complement(singleton_relation))))
| ~ spl0_28
| ~ spl0_333 ),
inference(duplicate_literal_removal,[],[f3414]) ).
fof(f3414,plain,
( subclass(singleton_relation,complement(compose(element_relation,complement(singleton_relation))))
| subclass(singleton_relation,complement(compose(element_relation,complement(singleton_relation))))
| ~ spl0_28
| ~ spl0_333 ),
inference(resolution,[],[f3325,f324]) ).
fof(f21776,plain,
( spl0_1035
| ~ spl0_313
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f3411,f3310,f3137,f21774]) ).
fof(f21774,plain,
( spl0_1035
<=> ! [X0] : subclass(intersection(singleton_relation,X0),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f3411,plain,
( ! [X0] : subclass(intersection(singleton_relation,X0),cross_product(universal_class,universal_class))
| ~ spl0_313
| ~ spl0_332 ),
inference(duplicate_literal_removal,[],[f3402]) ).
fof(f3402,plain,
( ! [X0] :
( subclass(intersection(singleton_relation,X0),cross_product(universal_class,universal_class))
| subclass(intersection(singleton_relation,X0),cross_product(universal_class,universal_class)) )
| ~ spl0_313
| ~ spl0_332 ),
inference(resolution,[],[f3311,f3138]) ).
fof(f21772,plain,
( spl0_1034
| ~ spl0_14
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f3390,f3214,f262,f21770]) ).
fof(f262,plain,
( spl0_14
<=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f3214,plain,
( spl0_328
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f3390,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| member(domain_of(X0),universal_class) )
| ~ spl0_14
| ~ spl0_328 ),
inference(resolution,[],[f3215,f264]) ).
fof(f264,plain,
( subclass(domain_relation,cross_product(universal_class,universal_class))
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f3215,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(X2),X1) )
| ~ spl0_328 ),
inference(avatar_component_clause,[],[f3214]) ).
fof(f21768,plain,
( spl0_1033
| ~ spl0_50
| ~ spl0_286
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f3381,f3210,f2735,f452,f21765]) ).
fof(f21765,plain,
( spl0_1033
<=> subclass(subset_relation,intersection(subset_relation,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f3381,plain,
( subclass(subset_relation,intersection(subset_relation,cross_product(universal_class,universal_class)))
| ~ spl0_50
| ~ spl0_286
| ~ spl0_327 ),
inference(forward_demodulation,[],[f3376,f453]) ).
fof(f3376,plain,
( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),subset_relation))
| ~ spl0_286
| ~ spl0_327 ),
inference(duplicate_literal_removal,[],[f3349]) ).
fof(f3349,plain,
( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),subset_relation))
| subclass(subset_relation,intersection(cross_product(universal_class,universal_class),subset_relation))
| ~ spl0_286
| ~ spl0_327 ),
inference(resolution,[],[f3211,f2736]) ).
fof(f21763,plain,
( spl0_1032
| ~ spl0_27
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f3297,f3149,f319,f21761]) ).
fof(f21761,plain,
( spl0_1032
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ subclass(X0,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f3297,plain,
( ! [X0,X1] :
( subclass(X0,X1)
| ~ subclass(X0,complement(X0)) )
| ~ spl0_27
| ~ spl0_316 ),
inference(duplicate_literal_removal,[],[f3268]) ).
fof(f3268,plain,
( ! [X0,X1] :
( subclass(X0,X1)
| ~ subclass(X0,complement(X0))
| subclass(X0,X1) )
| ~ spl0_27
| ~ spl0_316 ),
inference(resolution,[],[f3150,f320]) ).
fof(f21759,plain,
( spl0_1031
| ~ spl0_134
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3233,f3137,f1083,f21757]) ).
fof(f21757,plain,
( spl0_1031
<=> ! [X0] : subclass(intersection(subset_relation,X0),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f3233,plain,
( ! [X0] : subclass(intersection(subset_relation,X0),cross_product(universal_class,universal_class))
| ~ spl0_134
| ~ spl0_313 ),
inference(duplicate_literal_removal,[],[f3228]) ).
fof(f3228,plain,
( ! [X0] :
( subclass(intersection(subset_relation,X0),cross_product(universal_class,universal_class))
| subclass(intersection(subset_relation,X0),cross_product(universal_class,universal_class)) )
| ~ spl0_134
| ~ spl0_313 ),
inference(resolution,[],[f3138,f1084]) ).
fof(f21755,plain,
( spl0_1030
| ~ spl0_135
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3232,f3137,f1087,f21753]) ).
fof(f21753,plain,
( spl0_1030
<=> ! [X0] : subclass(intersection(X0,subset_relation),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f3232,plain,
( ! [X0] : subclass(intersection(X0,subset_relation),cross_product(universal_class,universal_class))
| ~ spl0_135
| ~ spl0_313 ),
inference(duplicate_literal_removal,[],[f3229]) ).
fof(f3229,plain,
( ! [X0] :
( subclass(intersection(X0,subset_relation),cross_product(universal_class,universal_class))
| subclass(intersection(X0,subset_relation),cross_product(universal_class,universal_class)) )
| ~ spl0_135
| ~ spl0_313 ),
inference(resolution,[],[f3138,f1088]) ).
fof(f21751,plain,
( ~ spl0_1029
| ~ spl0_20
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f3075,f3065,f287,f21748]) ).
fof(f287,plain,
( spl0_20
<=> ! [X4,X0] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f3065,plain,
( spl0_308
<=> member(regular(singleton_relation),complement(compose(element_relation,complement(singleton_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f3075,plain,
( ~ member(regular(singleton_relation),compose(element_relation,complement(singleton_relation)))
| ~ spl0_20
| ~ spl0_308 ),
inference(resolution,[],[f3067,f288]) ).
fof(f288,plain,
( ! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f3067,plain,
( member(regular(singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
| ~ spl0_308 ),
inference(avatar_component_clause,[],[f3065]) ).
fof(f21746,plain,
( spl0_231
| ~ spl0_1028
| ~ spl0_234
| ~ spl0_235
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3048,f2818,f2310,f2304,f21743,f2282]) ).
fof(f2282,plain,
( spl0_231
<=> null_class = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f21743,plain,
( spl0_1028
<=> subclass(singleton_relation,complement(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f3048,plain,
( ~ subclass(singleton_relation,complement(subset_relation))
| null_class = singleton_relation
| ~ spl0_234
| ~ spl0_235
| ~ spl0_292 ),
inference(forward_demodulation,[],[f3014,f2312]) ).
fof(f3014,plain,
( null_class = singleton_relation
| ~ subclass(identity_relation,complement(subset_relation))
| ~ spl0_234
| ~ spl0_235
| ~ spl0_292 ),
inference(forward_demodulation,[],[f2981,f2312]) ).
fof(f2981,plain,
( null_class = identity_relation
| ~ subclass(identity_relation,complement(subset_relation))
| ~ spl0_234
| ~ spl0_292 ),
inference(resolution,[],[f2819,f2306]) ).
fof(f21741,plain,
( spl0_1027
| ~ spl0_23
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f2992,f2818,f299,f21739]) ).
fof(f299,plain,
( spl0_23
<=> ! [X0] :
( null_class = X0
| member(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f2992,plain,
( ! [X0] :
( null_class = X0
| ~ subclass(X0,complement(X0)) )
| ~ spl0_23
| ~ spl0_292 ),
inference(duplicate_literal_removal,[],[f2964]) ).
fof(f2964,plain,
( ! [X0] :
( null_class = X0
| ~ subclass(X0,complement(X0))
| null_class = X0 )
| ~ spl0_23
| ~ spl0_292 ),
inference(resolution,[],[f2819,f300]) ).
fof(f300,plain,
( ! [X0] :
( member(regular(X0),X0)
| null_class = X0 )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f21737,plain,
( ~ spl0_1026
| spl0_231
| ~ spl0_232
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f2972,f2818,f2286,f2282,f21734]) ).
fof(f21734,plain,
( spl0_1026
<=> subclass(singleton_relation,complement(element_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f2286,plain,
( spl0_232
<=> member(regular(singleton_relation),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f2972,plain,
( null_class = singleton_relation
| ~ subclass(singleton_relation,complement(element_relation))
| ~ spl0_232
| ~ spl0_292 ),
inference(resolution,[],[f2819,f2288]) ).
fof(f2288,plain,
( member(regular(singleton_relation),element_relation)
| ~ spl0_232 ),
inference(avatar_component_clause,[],[f2286]) ).
fof(f21732,plain,
( spl0_652
| ~ spl0_1025
| ~ spl0_66
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f2584,f2499,f552,f21729,f9911]) ).
fof(f21729,plain,
( spl0_1025
<=> subclass(universal_class,complement(domain_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f2584,plain,
( ! [X0] :
( ~ subclass(universal_class,complement(domain_relation))
| ~ member(X0,universal_class) )
| ~ spl0_66
| ~ spl0_268 ),
inference(resolution,[],[f2500,f553]) ).
fof(f21727,plain,
( spl0_1024
| ~ spl0_106
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f2562,f2499,f802,f21725]) ).
fof(f21725,plain,
( spl0_1024
<=> ! [X0] :
( ~ subclass(universal_class,complement(X0))
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f2562,plain,
( ! [X0] :
( ~ subclass(universal_class,complement(X0))
| ~ subclass(universal_class,X0) )
| ~ spl0_106
| ~ spl0_268 ),
inference(resolution,[],[f2500,f803]) ).
fof(f21722,plain,
( spl0_1023
| ~ spl0_38
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2437,f2304,f372,f21720]) ).
fof(f21720,plain,
( spl0_1023
<=> ! [X0] :
( ~ subclass(subset_relation,X0)
| member(regular(identity_relation),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f2437,plain,
( ! [X0] :
( ~ subclass(subset_relation,X0)
| member(regular(identity_relation),X0) )
| ~ spl0_38
| ~ spl0_234 ),
inference(resolution,[],[f2306,f373]) ).
fof(f21718,plain,
( spl0_1022
| ~ spl0_38
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2327,f2286,f372,f21716]) ).
fof(f2327,plain,
( ! [X0] :
( ~ subclass(element_relation,X0)
| member(regular(singleton_relation),X0) )
| ~ spl0_38
| ~ spl0_232 ),
inference(resolution,[],[f2288,f373]) ).
fof(f21622,plain,
( spl0_1021
| ~ spl0_90
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1842,f1812,f686,f21620]) ).
fof(f21620,plain,
( spl0_1021
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f686,plain,
( spl0_90
<=> ! [X9,X11,X10] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1812,plain,
( spl0_204
<=> ! [X0,X3,X2,X1] :
( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f1842,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) )
| ~ spl0_90
| ~ spl0_204 ),
inference(resolution,[],[f1813,f687]) ).
fof(f687,plain,
( ! [X10,X11,X9] :
( member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10))
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| ~ operation(X10) )
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f686]) ).
fof(f1813,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) )
| ~ spl0_204 ),
inference(avatar_component_clause,[],[f1812]) ).
fof(f21618,plain,
( spl0_1020
| ~ spl0_90
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1816,f1803,f686,f21616]) ).
fof(f21616,plain,
( spl0_1020
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f1803,plain,
( spl0_202
<=> ! [X0,X3,X2,X1] :
( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f1816,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))) )
| ~ spl0_90
| ~ spl0_202 ),
inference(resolution,[],[f1804,f687]) ).
fof(f1804,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f1803]) ).
fof(f21553,plain,
( spl0_1019
| ~ spl0_111
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2128,f2124,f823,f21551]) ).
fof(f21551,plain,
( spl0_1019
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f2124,plain,
( spl0_221
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f2128,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),subset_relation) )
| ~ spl0_111
| ~ spl0_221 ),
inference(resolution,[],[f2125,f824]) ).
fof(f2125,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) )
| ~ spl0_221 ),
inference(avatar_component_clause,[],[f2124]) ).
fof(f21520,plain,
( spl0_1018
| ~ spl0_101
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1879,f1868,f750,f21518]) ).
fof(f21518,plain,
( spl0_1018
<=> ! [X4,X0,X3,X2,X1] :
( ~ subclass(composition_function,domain_of(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ homomorphism(X3,X0,X4)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))))))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))))))),universal_class),X0),universal_class)))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f750,plain,
( spl0_101
<=> ! [X10,X11,X0,X9,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1868,plain,
( spl0_205
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(composition_function,X2)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f1879,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(composition_function,domain_of(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ homomorphism(X3,X0,X4)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))))))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))))))),universal_class),X0),universal_class)))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) )
| ~ spl0_101
| ~ spl0_205 ),
inference(resolution,[],[f1869,f751]) ).
fof(f751,plain,
( ! [X10,X0,X11,X1,X9] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10))
| ~ homomorphism(X9,X10,X11)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class))))))) )
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f750]) ).
fof(f1869,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2)
| ~ subclass(composition_function,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f1868]) ).
fof(f21490,plain,
( spl0_1017
| ~ spl0_197
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2016,f1994,f1704,f21488]) ).
fof(f21488,plain,
( spl0_1017
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(successor_relation))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f1704,plain,
( spl0_197
<=> ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1994,plain,
( spl0_211
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f2016,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(successor_relation))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) )
| ~ spl0_197
| ~ spl0_211 ),
inference(resolution,[],[f1995,f1705]) ).
fof(f1705,plain,
( ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f1704]) ).
fof(f1995,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_211 ),
inference(avatar_component_clause,[],[f1994]) ).
fof(f21485,plain,
( spl0_1016
| ~ spl0_43
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2240,f2223,f393,f21482]) ).
fof(f21482,plain,
( spl0_1016
<=> subclass(identity_relation,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f2240,plain,
( subclass(identity_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_43
| ~ spl0_223 ),
inference(superposition,[],[f2224,f395]) ).
fof(f21417,plain,
( spl0_1015
| ~ spl0_77
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2127,f2124,f613,f21415]) ).
fof(f21415,plain,
( spl0_1015
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f613,plain,
( spl0_77
<=> ! [X0,X3,X2,X1] :
( ~ member(X2,X0)
| ~ member(X3,X1)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f2127,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_77
| ~ spl0_221 ),
inference(resolution,[],[f2125,f614]) ).
fof(f614,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
| ~ member(X3,X1)
| ~ member(X2,X0) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f21403,plain,
( spl0_1014
| ~ spl0_40
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2131,f2124,f380,f21401]) ).
fof(f21401,plain,
( spl0_1014
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ operation(X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f380,plain,
( spl0_40
<=> ! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f2131,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ operation(X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_40
| ~ spl0_221 ),
inference(superposition,[],[f2125,f381]) ).
fof(f381,plain,
( ! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f21373,plain,
( spl0_1013
| ~ spl0_205
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2002,f1994,f1868,f21371]) ).
fof(f21371,plain,
( spl0_1013
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(composition_function,X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f2002,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(composition_function,X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
| ~ spl0_205
| ~ spl0_211 ),
inference(resolution,[],[f1995,f1869]) ).
fof(f21343,plain,
( spl0_1012
| ~ spl0_92
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2021,f1994,f696,f21341]) ).
fof(f21341,plain,
( spl0_1012
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(composition_function))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f696,plain,
( spl0_92
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f2021,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(composition_function))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
| ~ spl0_92
| ~ spl0_211 ),
inference(resolution,[],[f1995,f697]) ).
fof(f697,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f696]) ).
fof(f21326,plain,
( spl0_1011
| ~ spl0_101
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1752,f1745,f750,f21324]) ).
fof(f21324,plain,
( spl0_1011
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(X3))
| ~ operation(X2)
| ~ homomorphism(X4,X3,X5)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class)))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))))))),universal_class),X5),universal_class))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f1745,plain,
( spl0_199
<=> ! [X0,X3,X2,X1] :
( ~ operation(X0)
| ~ compatible(X1,X2,X0)
| homomorphism(X1,X2,X0)
| ~ operation(X2)
| ~ subclass(domain_of(X2),X3)
| member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f1752,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(X3))
| ~ operation(X2)
| ~ homomorphism(X4,X3,X5)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class)))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))))))),universal_class),X5),universal_class))))))) )
| ~ spl0_101
| ~ spl0_199 ),
inference(resolution,[],[f1746,f751]) ).
fof(f1746,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3)
| ~ compatible(X1,X2,X0)
| homomorphism(X1,X2,X0)
| ~ operation(X2)
| ~ subclass(domain_of(X2),X3)
| ~ operation(X0) )
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f1745]) ).
fof(f21314,plain,
( spl0_1010
| ~ spl0_41
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2239,f2223,f384,f21311]) ).
fof(f21311,plain,
( spl0_1010
<=> subclass(singleton_relation,complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f2239,plain,
( subclass(singleton_relation,complement(compose(element_relation,complement(identity_relation))))
| ~ spl0_41
| ~ spl0_223 ),
inference(superposition,[],[f2224,f386]) ).
fof(f21309,plain,
( spl0_1009
| ~ spl0_198
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2118,f2110,f1711,f21307]) ).
fof(f21307,plain,
( spl0_1009
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(regular(cross_product(X0,X1)),universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
| ~ homomorphism(X3,X2,X4)
| null_class = intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f1711,plain,
( spl0_198
<=> ! [X0,X1] :
( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f2110,plain,
( spl0_219
<=> ! [X4,X0,X3,X2,X1] :
( ~ homomorphism(X0,X1,X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
| null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f2118,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(regular(cross_product(X0,X1)),universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
| ~ homomorphism(X3,X2,X4)
| null_class = intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2)
| cross_product(X0,X1) = null_class )
| ~ spl0_198
| ~ spl0_219 ),
inference(superposition,[],[f2111,f1712]) ).
fof(f1712,plain,
( ! [X0,X1] :
( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
| cross_product(X0,X1) = null_class )
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f1711]) ).
fof(f2111,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
| ~ homomorphism(X0,X1,X2)
| null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) )
| ~ spl0_219 ),
inference(avatar_component_clause,[],[f2110]) ).
fof(f21291,plain,
( spl0_1008
| ~ spl0_101
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1731,f1711,f750,f21289]) ).
fof(f21289,plain,
( spl0_1008
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(regular(cross_product(X0,X1)),domain_of(X2))
| ~ homomorphism(X3,X2,X4)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f1731,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(regular(cross_product(X0,X1)),domain_of(X2))
| ~ homomorphism(X3,X2,X4)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
| cross_product(X0,X1) = null_class )
| ~ spl0_101
| ~ spl0_198 ),
inference(superposition,[],[f751,f1712]) ).
fof(f21006,plain,
( spl0_1007
| ~ spl0_195
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1855,f1812,f1656,f21004]) ).
fof(f21004,plain,
( spl0_1007
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f1656,plain,
( spl0_195
<=> ! [X0,X1] :
( ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = null_class
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f1855,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),universal_class) )
| ~ spl0_195
| ~ spl0_204 ),
inference(resolution,[],[f1813,f1657]) ).
fof(f1657,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1)
| intersection(X0,X1) = null_class
| ~ member(intersection(X0,X1),universal_class) )
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f1656]) ).
fof(f20987,plain,
( spl0_1006
| ~ spl0_196
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1847,f1812,f1660,f20985]) ).
fof(f20985,plain,
( spl0_1006
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)
| ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f1660,plain,
( spl0_196
<=> ! [X0,X1] :
( ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = null_class
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f1847,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)
| ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),universal_class) )
| ~ spl0_196
| ~ spl0_204 ),
inference(resolution,[],[f1813,f1661]) ).
fof(f1661,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0)
| intersection(X0,X1) = null_class
| ~ member(intersection(X0,X1),universal_class) )
| ~ spl0_196 ),
inference(avatar_component_clause,[],[f1660]) ).
fof(f20983,plain,
( spl0_1005
| ~ spl0_195
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1829,f1803,f1656,f20981]) ).
fof(f20981,plain,
( spl0_1005
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f1829,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),universal_class) )
| ~ spl0_195
| ~ spl0_202 ),
inference(resolution,[],[f1804,f1657]) ).
fof(f20979,plain,
( spl0_1004
| ~ spl0_196
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1821,f1803,f1660,f20977]) ).
fof(f20977,plain,
( spl0_1004
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)
| ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f1821,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)
| ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class) )
| ~ spl0_196
| ~ spl0_202 ),
inference(resolution,[],[f1804,f1661]) ).
fof(f20975,plain,
( spl0_1003
| ~ spl0_93
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1692,f1660,f702,f20973]) ).
fof(f20973,plain,
( spl0_1003
<=> ! [X0,X3,X2,X1] :
( null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f702,plain,
( spl0_93
<=> ! [X4,X7,X5,X1] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f1692,plain,
( ! [X2,X3,X0,X1] :
( null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_196 ),
inference(resolution,[],[f1661,f703]) ).
fof(f703,plain,
( ! [X1,X7,X4,X5] :
( ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class)))))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f702]) ).
fof(f20971,plain,
( spl0_1002
| ~ spl0_93
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f1672,f1656,f702,f20969]) ).
fof(f20969,plain,
( spl0_1002
<=> ! [X0,X3,X2,X1] :
( null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),universal_class)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f1672,plain,
( ! [X2,X3,X0,X1] :
( null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),universal_class)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_195 ),
inference(resolution,[],[f1657,f703]) ).
fof(f20967,plain,
( spl0_1001
| ~ spl0_9
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2113,f2110,f240,f20965]) ).
fof(f20965,plain,
( spl0_1001
<=> ! [X2,X4,X0,X3,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class)))))))
| ~ homomorphism(X3,X2,X4)
| null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f2113,plain,
( ! [X2,X3,X0,X1,X4] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class)))))))
| ~ homomorphism(X3,X2,X4)
| null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2) )
| ~ spl0_9
| ~ spl0_219 ),
inference(resolution,[],[f2111,f241]) ).
fof(f20963,plain,
( spl0_1000
| ~ spl0_101
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1413,f1369,f750,f20961]) ).
fof(f20961,plain,
( spl0_1000
<=> ! [X0,X3,X2,X1] :
( ~ subclass(domain_relation,domain_of(X0))
| ~ member(X1,universal_class)
| ~ homomorphism(X2,X0,X3)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))),universal_class),X0),universal_class)))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f1413,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(domain_relation,domain_of(X0))
| ~ member(X1,universal_class)
| ~ homomorphism(X2,X0,X3)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))),universal_class),X0),universal_class)))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) )
| ~ spl0_101
| ~ spl0_165 ),
inference(resolution,[],[f1370,f751]) ).
fof(f20932,plain,
( spl0_999
| ~ spl0_23
| ~ spl0_130
| ~ spl0_888 ),
inference(avatar_split_clause,[],[f17186,f17013,f1012,f299,f20930]) ).
fof(f20930,plain,
( spl0_999
<=> ! [X0,X1] :
( ~ subclass(X0,null_class)
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f17013,plain,
( spl0_888
<=> ! [X0] : ~ member(X0,domain_of(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f17186,plain,
( ! [X0,X1] :
( ~ subclass(X0,null_class)
| subclass(X0,X1) )
| ~ spl0_23
| ~ spl0_130
| ~ spl0_888 ),
inference(forward_demodulation,[],[f17131,f17110]) ).
fof(f17110,plain,
( null_class = domain_of(null_class)
| ~ spl0_23
| ~ spl0_888 ),
inference(resolution,[],[f17014,f300]) ).
fof(f17014,plain,
( ! [X0] : ~ member(X0,domain_of(null_class))
| ~ spl0_888 ),
inference(avatar_component_clause,[],[f17013]) ).
fof(f17131,plain,
( ! [X0,X1] :
( ~ subclass(X0,domain_of(null_class))
| subclass(X0,X1) )
| ~ spl0_130
| ~ spl0_888 ),
inference(resolution,[],[f17014,f1013]) ).
fof(f20928,plain,
( spl0_998
| ~ spl0_235
| ~ spl0_997 ),
inference(avatar_split_clause,[],[f20924,f20921,f2310,f20926]) ).
fof(f20926,plain,
( spl0_998
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),singleton_relation)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class),X2),universal_class)))))))
| ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f20921,plain,
( spl0_997
<=> ! [X0,X3,X2,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class),X2),universal_class)))))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation)
| ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f20924,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),singleton_relation)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class),X2),universal_class)))))))
| ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3) )
| ~ spl0_235
| ~ spl0_997 ),
inference(forward_demodulation,[],[f20922,f2312]) ).
fof(f20922,plain,
( ! [X2,X3,X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class),X2),universal_class)))))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation)
| ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3) )
| ~ spl0_997 ),
inference(avatar_component_clause,[],[f20921]) ).
fof(f20923,plain,
( spl0_997
| ~ spl0_50
| ~ spl0_101
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1002,f959,f750,f452,f20921]) ).
fof(f959,plain,
( spl0_125
<=> ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1002,plain,
( ! [X2,X3,X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class),X2),universal_class)))))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation)
| ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3) )
| ~ spl0_50
| ~ spl0_101
| ~ spl0_125 ),
inference(forward_demodulation,[],[f1000,f453]) ).
fof(f1000,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation)
| ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),flip(cross_product(subset_relation,universal_class))),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),flip(cross_product(subset_relation,universal_class))),universal_class)))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) )
| ~ spl0_101
| ~ spl0_125 ),
inference(resolution,[],[f960,f751]) ).
fof(f960,plain,
( ! [X0] :
( member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,identity_relation) )
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f959]) ).
fof(f20851,plain,
( spl0_996
| ~ spl0_84
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1846,f1812,f654,f20849]) ).
fof(f20849,plain,
( spl0_996
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f654,plain,
( spl0_84
<=> ! [X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
| ~ member(X1,universal_class)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1846,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))) )
| ~ spl0_84
| ~ spl0_204 ),
inference(resolution,[],[f1813,f655]) ).
fof(f655,plain,
( ! [X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
| ~ member(X1,universal_class)
| null_class = X1 )
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f654]) ).
fof(f20847,plain,
( spl0_995
| ~ spl0_84
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1820,f1803,f654,f20845]) ).
fof(f20845,plain,
( spl0_995
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f1820,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_84
| ~ spl0_202 ),
inference(resolution,[],[f1804,f655]) ).
fof(f20797,plain,
( spl0_994
| ~ spl0_111
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2101,f2097,f823,f20795]) ).
fof(f20795,plain,
( spl0_994
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f2097,plain,
( spl0_218
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f2101,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),subset_relation) )
| ~ spl0_111
| ~ spl0_218 ),
inference(resolution,[],[f2098,f824]) ).
fof(f2098,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f2097]) ).
fof(f20793,plain,
( spl0_993
| ~ spl0_101
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f830,f802,f750,f20791]) ).
fof(f20791,plain,
( spl0_993
<=> ! [X4,X0,X3,X2,X1] :
( ~ subclass(universal_class,domain_of(X0))
| ~ homomorphism(X1,X0,X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class)))))))),universal_class),X1),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))))))),universal_class),X2),universal_class))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f830,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,domain_of(X0))
| ~ homomorphism(X1,X0,X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class)))))))),universal_class),X1),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))))))),universal_class),X2),universal_class))))))) )
| ~ spl0_101
| ~ spl0_106 ),
inference(resolution,[],[f803,f751]) ).
fof(f20788,plain,
( spl0_992
| ~ spl0_23
| ~ spl0_376
| ~ spl0_888 ),
inference(avatar_split_clause,[],[f17159,f17013,f3818,f299,f20786]) ).
fof(f20786,plain,
( spl0_992
<=> ! [X0] : subclass(intersection(universal_class,X0),complement(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f3818,plain,
( spl0_376
<=> ! [X0,X1] :
( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
| subclass(intersection(universal_class,X0),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f17159,plain,
( ! [X0] : subclass(intersection(universal_class,X0),complement(null_class))
| ~ spl0_23
| ~ spl0_376
| ~ spl0_888 ),
inference(forward_demodulation,[],[f17116,f17110]) ).
fof(f17116,plain,
( ! [X0] : subclass(intersection(universal_class,X0),complement(domain_of(null_class)))
| ~ spl0_376
| ~ spl0_888 ),
inference(resolution,[],[f17014,f3819]) ).
fof(f3819,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
| subclass(intersection(universal_class,X0),complement(X1)) )
| ~ spl0_376 ),
inference(avatar_component_clause,[],[f3818]) ).
fof(f20784,plain,
( ~ spl0_990
| spl0_991
| ~ spl0_40
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2134,f2124,f380,f20782,f20778]) ).
fof(f20778,plain,
( spl0_990
<=> operation(domain_of(flip(cross_product(null_class,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f20782,plain,
( spl0_991
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3))))))),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)
| homomorphism(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)
| ~ compatible(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)
| ~ operation(X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f2134,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
| ~ operation(X3)
| ~ compatible(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)
| homomorphism(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(null_class,universal_class))))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
| ~ spl0_40
| ~ spl0_221 ),
inference(superposition,[],[f2125,f381]) ).
fof(f20770,plain,
( spl0_989
| ~ spl0_40
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2104,f2097,f380,f20768]) ).
fof(f20768,plain,
( spl0_989
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f2104,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_40
| ~ spl0_218 ),
inference(superposition,[],[f2098,f381]) ).
fof(f20624,plain,
( spl0_988
| ~ spl0_95
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1884,f1868,f723,f20622]) ).
fof(f20622,plain,
( spl0_988
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),unordered_pair(X1,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f723,plain,
( spl0_95
<=> ! [X3,X0,X6,X2] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1884,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),unordered_pair(X1,X1))),X0) )
| ~ spl0_95
| ~ spl0_205 ),
inference(resolution,[],[f1869,f724]) ).
fof(f724,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f723]) ).
fof(f20572,plain,
( spl0_987
| ~ spl0_77
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2100,f2097,f613,f20570]) ).
fof(f20570,plain,
( spl0_987
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f2100,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_77
| ~ spl0_218 ),
inference(resolution,[],[f2098,f614]) ).
fof(f20568,plain,
( spl0_985
| ~ spl0_986
| ~ spl0_99
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1886,f1868,f739,f20565,f20562]) ).
fof(f20562,plain,
( spl0_985
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2))))))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2))))))),flip(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f20565,plain,
( spl0_986
<=> subclass(composition_function,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f739,plain,
( spl0_99
<=> ! [X3,X0,X6,X2] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1886,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2))))))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2))))))),X3) )
| ~ spl0_99
| ~ spl0_205 ),
inference(resolution,[],[f1869,f740]) ).
fof(f740,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f20533,plain,
( spl0_984
| ~ spl0_23
| ~ spl0_375
| ~ spl0_888 ),
inference(avatar_split_clause,[],[f17155,f17013,f3814,f299,f20531]) ).
fof(f20531,plain,
( spl0_984
<=> ! [X0] : subclass(intersection(X0,universal_class),complement(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f3814,plain,
( spl0_375
<=> ! [X0,X1] :
( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
| subclass(intersection(X0,universal_class),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f17155,plain,
( ! [X0] : subclass(intersection(X0,universal_class),complement(null_class))
| ~ spl0_23
| ~ spl0_375
| ~ spl0_888 ),
inference(forward_demodulation,[],[f17114,f17110]) ).
fof(f17114,plain,
( ! [X0] : subclass(intersection(X0,universal_class),complement(domain_of(null_class)))
| ~ spl0_375
| ~ spl0_888 ),
inference(resolution,[],[f17014,f3815]) ).
fof(f3815,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
| subclass(intersection(X0,universal_class),complement(X1)) )
| ~ spl0_375 ),
inference(avatar_component_clause,[],[f3814]) ).
fof(f20529,plain,
( spl0_983
| ~ spl0_186
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2020,f1994,f1578,f20527]) ).
fof(f20527,plain,
( spl0_983
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose_class(X0)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f1578,plain,
( spl0_186
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
| ~ member(compose(X1,X0),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f2020,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose_class(X0)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class) )
| ~ spl0_186
| ~ spl0_211 ),
inference(resolution,[],[f1995,f1579]) ).
fof(f1579,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
| ~ member(compose(X1,X0),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_186 ),
inference(avatar_component_clause,[],[f1578]) ).
fof(f20507,plain,
( spl0_982
| ~ spl0_204
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1899,f1868,f1812,f20505]) ).
fof(f20505,plain,
( spl0_982
<=> ! [X4,X0,X3,X2,X1] :
( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X0,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f1899,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X0,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_204
| ~ spl0_205 ),
inference(resolution,[],[f1869,f1813]) ).
fof(f20503,plain,
( spl0_981
| ~ spl0_202
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1898,f1868,f1803,f20501]) ).
fof(f20501,plain,
( spl0_981
<=> ! [X4,X0,X3,X2,X1] :
( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X2,X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f1898,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X2,X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_202
| ~ spl0_205 ),
inference(resolution,[],[f1869,f1804]) ).
fof(f20499,plain,
( spl0_980
| ~ spl0_93
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1897,f1868,f702,f20497]) ).
fof(f20497,plain,
( spl0_980
<=> ! [X4,X0,X3,X2,X1] :
( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f1897,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_205 ),
inference(resolution,[],[f1869,f703]) ).
fof(f20477,plain,
( spl0_979
| ~ spl0_100
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1730,f1711,f745,f20475]) ).
fof(f20475,plain,
( spl0_979
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ member(first(regular(cross_product(X0,X1))),domain_of(X2))
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))))))))),application_function)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f745,plain,
( spl0_100
<=> ! [X4,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(X1,domain_of(X0))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1730,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ member(first(regular(cross_product(X0,X1))),domain_of(X2))
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))))))))),application_function)
| cross_product(X0,X1) = null_class )
| ~ spl0_100
| ~ spl0_198 ),
inference(superposition,[],[f746,f1712]) ).
fof(f746,plain,
( ! [X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ member(X1,domain_of(X0))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function) )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f745]) ).
fof(f20426,plain,
( spl0_978
| ~ spl0_134
| ~ spl0_888 ),
inference(avatar_split_clause,[],[f17103,f17013,f1083,f20424]) ).
fof(f20424,plain,
( spl0_978
<=> ! [X0,X1] : subclass(intersection(domain_of(null_class),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f17103,plain,
( ! [X0,X1] : subclass(intersection(domain_of(null_class),X0),X1)
| ~ spl0_134
| ~ spl0_888 ),
inference(resolution,[],[f17014,f1084]) ).
fof(f20422,plain,
( spl0_977
| ~ spl0_205
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2025,f1998,f1868,f20420]) ).
fof(f20420,plain,
( spl0_977
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2))))))),flip(X3))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(composition_function,X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f1998,plain,
( spl0_212
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f2025,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2))))))),flip(X3))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(composition_function,X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
| ~ spl0_205
| ~ spl0_212 ),
inference(resolution,[],[f1999,f1869]) ).
fof(f1999,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f1998]) ).
fof(f20378,plain,
( spl0_976
| ~ spl0_165
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2001,f1994,f1369,f20376]) ).
fof(f20376,plain,
( spl0_976
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(X2))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ subclass(domain_relation,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f2001,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(X2))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ subclass(domain_relation,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) )
| ~ spl0_165
| ~ spl0_211 ),
inference(resolution,[],[f1995,f1370]) ).
fof(f20374,plain,
( spl0_975
| ~ spl0_79
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1685,f1660,f628,f20372]) ).
fof(f20372,plain,
( spl0_975
<=> ! [X2,X0,X1] :
( null_class = intersection(cross_product(X0,X1),X2)
| ~ member(intersection(cross_product(X0,X1),X2),universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f628,plain,
( spl0_79
<=> ! [X4,X0,X1] :
( ~ member(X4,cross_product(X0,X1))
| unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1685,plain,
( ! [X2,X0,X1] :
( null_class = intersection(cross_product(X0,X1),X2)
| ~ member(intersection(cross_product(X0,X1),X2),universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))))) )
| ~ spl0_79
| ~ spl0_196 ),
inference(resolution,[],[f1661,f629]) ).
fof(f629,plain,
( ! [X0,X1,X4] :
( ~ member(X4,cross_product(X0,X1))
| unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 )
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f628]) ).
fof(f20370,plain,
( spl0_974
| ~ spl0_79
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f1665,f1656,f628,f20368]) ).
fof(f20368,plain,
( spl0_974
<=> ! [X2,X0,X1] :
( null_class = intersection(X0,cross_product(X1,X2))
| ~ member(intersection(X0,cross_product(X1,X2)),universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f1665,plain,
( ! [X2,X0,X1] :
( null_class = intersection(X0,cross_product(X1,X2))
| ~ member(intersection(X0,cross_product(X1,X2)),universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))))) )
| ~ spl0_79
| ~ spl0_195 ),
inference(resolution,[],[f1657,f629]) ).
fof(f20321,plain,
( spl0_973
| ~ spl0_92
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2044,f1998,f696,f20319]) ).
fof(f20319,plain,
( spl0_973
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2))))))),flip(composition_function))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f2044,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2))))))),flip(composition_function))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
| ~ spl0_92
| ~ spl0_212 ),
inference(resolution,[],[f1999,f697]) ).
fof(f20298,plain,
( spl0_972
| ~ spl0_287
| ~ spl0_888 ),
inference(avatar_split_clause,[],[f17105,f17013,f2739,f20295]) ).
fof(f20295,plain,
( spl0_972
<=> subclass(universal_class,complement(domain_of(null_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f17105,plain,
( subclass(universal_class,complement(domain_of(null_class)))
| ~ spl0_287
| ~ spl0_888 ),
inference(resolution,[],[f17014,f2740]) ).
fof(f20267,plain,
( spl0_971
| ~ spl0_198
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2065,f2051,f1711,f20265]) ).
fof(f20265,plain,
( spl0_971
<=> ! [X2,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))))))))),application_function)
| ~ member(first(regular(cross_product(X0,X1))),domain_of(X2))
| ~ member(X2,universal_class)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f2051,plain,
( spl0_213
<=> ! [X2,X0,X1] :
( ~ member(X0,domain_of(X1))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f2065,plain,
( ! [X2,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))))))))),application_function)
| ~ member(first(regular(cross_product(X0,X1))),domain_of(X2))
| ~ member(X2,universal_class)
| cross_product(X0,X1) = null_class )
| ~ spl0_198
| ~ spl0_213 ),
inference(superposition,[],[f2052,f1712]) ).
fof(f2052,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
| ~ member(X0,domain_of(X1))
| ~ member(X1,universal_class) )
| ~ spl0_213 ),
inference(avatar_component_clause,[],[f2051]) ).
fof(f20263,plain,
( spl0_970
| ~ spl0_66
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2022,f1994,f552,f20261]) ).
fof(f20261,plain,
( spl0_970
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(domain_relation))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f2022,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(domain_relation))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) )
| ~ spl0_66
| ~ spl0_211 ),
inference(resolution,[],[f1995,f553]) ).
fof(f20085,plain,
( spl0_969
| ~ spl0_199
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2064,f2051,f1745,f20083]) ).
fof(f20083,plain,
( spl0_969
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(not_homomorphism1(X1,X2,X3),domain_of(X0))
| ~ member(X0,universal_class)
| ~ compatible(X1,X2,X3)
| homomorphism(X1,X2,X3)
| ~ operation(X2)
| ~ subclass(domain_of(X2),cross_product(universal_class,universal_class))
| ~ operation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f2064,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(not_homomorphism1(X1,X2,X3),domain_of(X0))
| ~ member(X0,universal_class)
| ~ compatible(X1,X2,X3)
| homomorphism(X1,X2,X3)
| ~ operation(X2)
| ~ subclass(domain_of(X2),cross_product(universal_class,universal_class))
| ~ operation(X3) )
| ~ spl0_199
| ~ spl0_213 ),
inference(resolution,[],[f2052,f1746]) ).
fof(f20081,plain,
( spl0_968
| ~ spl0_209
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2041,f1998,f1935,f20079]) ).
fof(f20079,plain,
( spl0_968
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class)),X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f1935,plain,
( spl0_209
<=> ! [X2,X0,X1] :
( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f2041,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class)),X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class) )
| ~ spl0_209
| ~ spl0_212 ),
inference(resolution,[],[f1999,f1936]) ).
fof(f1936,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
| ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
| ~ spl0_209 ),
inference(avatar_component_clause,[],[f1935]) ).
fof(f19750,plain,
( spl0_967
| ~ spl0_70
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2037,f1998,f568,f19748]) ).
fof(f19748,plain,
( spl0_967
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class)
| null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2)))),universal_class),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f568,plain,
( spl0_70
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f2037,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class)
| null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2)))),universal_class),X3) )
| ~ spl0_70
| ~ spl0_212 ),
inference(resolution,[],[f1999,f569]) ).
fof(f569,plain,
( ! [X0,X4] :
( member(X4,domain_of(X0))
| ~ member(X4,universal_class)
| null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) )
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f568]) ).
fof(f19746,plain,
( spl0_966
| ~ spl0_209
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2018,f1994,f1935,f19744]) ).
fof(f19744,plain,
( spl0_966
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f2018,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) )
| ~ spl0_209
| ~ spl0_211 ),
inference(resolution,[],[f1995,f1936]) ).
fof(f19742,plain,
( spl0_965
| ~ spl0_70
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2014,f1994,f568,f19740]) ).
fof(f19740,plain,
( spl0_965
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class)
| null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0)))),universal_class),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f2014,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class)
| null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0)))),universal_class),X3) )
| ~ spl0_70
| ~ spl0_211 ),
inference(resolution,[],[f1995,f569]) ).
fof(f19716,plain,
( spl0_964
| ~ spl0_198
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2046,f1998,f1711,f19714]) ).
fof(f19714,plain,
( spl0_964
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),flip(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f2046,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),flip(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
| cross_product(X0,X1) = null_class )
| ~ spl0_198
| ~ spl0_212 ),
inference(superposition,[],[f1999,f1712]) ).
fof(f19712,plain,
( spl0_963
| ~ spl0_158
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1901,f1868,f1294,f19710]) ).
fof(f19710,plain,
( spl0_963
<=> ! [X0,X1] :
( ~ subclass(composition_function,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f1294,plain,
( spl0_158
<=> ! [X0] :
( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1901,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),universal_class) )
| ~ spl0_158
| ~ spl0_205 ),
inference(resolution,[],[f1869,f1295]) ).
fof(f1295,plain,
( ! [X0] :
( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f1294]) ).
fof(f19667,plain,
( spl0_962
| ~ spl0_197
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2048,f1998,f1704,f19665]) ).
fof(f19665,plain,
( spl0_962
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))))))))),flip(successor_relation))
| ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f2048,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))))))))),flip(successor_relation))
| ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
| ~ spl0_197
| ~ spl0_212 ),
inference(duplicate_literal_removal,[],[f2039]) ).
fof(f2039,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))))))))),flip(successor_relation))
| ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
| ~ spl0_197
| ~ spl0_212 ),
inference(resolution,[],[f1999,f1705]) ).
fof(f19604,plain,
( spl0_961
| ~ spl0_199
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1861,f1812,f1745,f19602]) ).
fof(f19602,plain,
( spl0_961
<=> ! [X3,X4,X0,X5,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
| ~ compatible(X1,X2,X3)
| homomorphism(X1,X2,X3)
| ~ operation(X2)
| ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X5),universal_class)))),universal_class)),universal_class)))))
| ~ operation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f1861,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
| ~ compatible(X1,X2,X3)
| homomorphism(X1,X2,X3)
| ~ operation(X2)
| ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X5),universal_class)))),universal_class)),universal_class)))))
| ~ operation(X3) )
| ~ spl0_199
| ~ spl0_204 ),
inference(resolution,[],[f1813,f1746]) ).
fof(f19600,plain,
( spl0_960
| ~ spl0_199
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1835,f1803,f1745,f19598]) ).
fof(f19598,plain,
( spl0_960
<=> ! [X3,X4,X0,X5,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
| ~ compatible(X1,X2,X3)
| homomorphism(X1,X2,X3)
| ~ operation(X2)
| ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X4),universal_class)))))
| ~ operation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f1835,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
| ~ compatible(X1,X2,X3)
| homomorphism(X1,X2,X3)
| ~ operation(X2)
| ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X4),universal_class)))))
| ~ operation(X3) )
| ~ spl0_199
| ~ spl0_202 ),
inference(resolution,[],[f1804,f1746]) ).
fof(f19596,plain,
( spl0_959
| ~ spl0_93
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1766,f1745,f702,f19594]) ).
fof(f19594,plain,
( spl0_959
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X4),universal_class)))),universal_class),X5),universal_class)))))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),compose(X5,X4))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f1766,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X4),universal_class)))),universal_class),X5),universal_class)))))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),compose(X5,X4))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_199 ),
inference(resolution,[],[f1746,f703]) ).
fof(f19546,plain,
( spl0_958
| ~ spl0_786
| ~ spl0_869
| ~ spl0_957 ),
inference(avatar_split_clause,[],[f19542,f19538,f16536,f14703,f19544]) ).
fof(f19544,plain,
( spl0_958
<=> ! [X0,X3,X2,X1] :
( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f16536,plain,
( spl0_869
<=> ! [X0] : null_class = intersection(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f19538,plain,
( spl0_957
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f19542,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) )
| ~ spl0_786
| ~ spl0_869
| ~ spl0_957 ),
inference(forward_demodulation,[],[f19541,f16537]) ).
fof(f16537,plain,
( ! [X0] : null_class = intersection(null_class,X0)
| ~ spl0_869 ),
inference(avatar_component_clause,[],[f16536]) ).
fof(f19541,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(null_class,X3),universal_class)))))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) )
| ~ spl0_786
| ~ spl0_957 ),
inference(forward_demodulation,[],[f19539,f14705]) ).
fof(f19539,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) )
| ~ spl0_957 ),
inference(avatar_component_clause,[],[f19538]) ).
fof(f19540,plain,
( spl0_957
| ~ spl0_206
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2040,f1998,f1906,f19538]) ).
fof(f1906,plain,
( spl0_206
<=> ! [X2,X0,X1] :
( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f2040,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) )
| ~ spl0_206
| ~ spl0_212 ),
inference(resolution,[],[f1999,f1907]) ).
fof(f1907,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_206 ),
inference(avatar_component_clause,[],[f1906]) ).
fof(f19490,plain,
( spl0_956
| ~ spl0_786
| ~ spl0_869
| ~ spl0_954 ),
inference(avatar_split_clause,[],[f19481,f19477,f16536,f14703,f19488]) ).
fof(f19488,plain,
( spl0_956
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f19477,plain,
( spl0_954
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f19481,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) )
| ~ spl0_786
| ~ spl0_869
| ~ spl0_954 ),
inference(forward_demodulation,[],[f19480,f16537]) ).
fof(f19480,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(null_class,X3),universal_class)))))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) )
| ~ spl0_786
| ~ spl0_954 ),
inference(forward_demodulation,[],[f19478,f14705]) ).
fof(f19478,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) )
| ~ spl0_954 ),
inference(avatar_component_clause,[],[f19477]) ).
fof(f19486,plain,
( spl0_955
| ~ spl0_55
| ~ spl0_938 ),
inference(avatar_split_clause,[],[f18953,f18827,f477,f19483]) ).
fof(f19483,plain,
( spl0_955
<=> universal_class = complement(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f477,plain,
( spl0_55
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f18827,plain,
( spl0_938
<=> subclass(universal_class,complement(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f18953,plain,
( universal_class = complement(null_class)
| ~ spl0_55
| ~ spl0_938 ),
inference(resolution,[],[f18829,f478]) ).
fof(f478,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f18829,plain,
( subclass(universal_class,complement(null_class))
| ~ spl0_938 ),
inference(avatar_component_clause,[],[f18827]) ).
fof(f19479,plain,
( spl0_954
| ~ spl0_206
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2017,f1994,f1906,f19477]) ).
fof(f2017,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) )
| ~ spl0_206
| ~ spl0_211 ),
inference(resolution,[],[f1995,f1907]) ).
fof(f19269,plain,
( spl0_953
| ~ spl0_135
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1850,f1812,f1087,f19267]) ).
fof(f19267,plain,
( spl0_953
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),cross_product(universal_class,universal_class))
| subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f1850,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),cross_product(universal_class,universal_class))
| subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4) )
| ~ spl0_135
| ~ spl0_204 ),
inference(resolution,[],[f1813,f1088]) ).
fof(f19265,plain,
( spl0_952
| ~ spl0_134
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1844,f1812,f1083,f19263]) ).
fof(f19263,plain,
( spl0_952
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
| subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f1844,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
| subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4) )
| ~ spl0_134
| ~ spl0_204 ),
inference(resolution,[],[f1813,f1084]) ).
fof(f19261,plain,
( spl0_951
| ~ spl0_135
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1824,f1803,f1087,f19259]) ).
fof(f19259,plain,
( spl0_951
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class))
| subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f1824,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class))
| subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4) )
| ~ spl0_135
| ~ spl0_202 ),
inference(resolution,[],[f1804,f1088]) ).
fof(f19256,plain,
( spl0_950
| ~ spl0_228
| ~ spl0_938 ),
inference(avatar_split_clause,[],[f18952,f18827,f2265,f19253]) ).
fof(f19253,plain,
( spl0_950
<=> member(null_class,complement(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f2265,plain,
( spl0_228
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f18952,plain,
( member(null_class,complement(null_class))
| ~ spl0_228
| ~ spl0_938 ),
inference(resolution,[],[f18829,f2266]) ).
fof(f2266,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(null_class,X0) )
| ~ spl0_228 ),
inference(avatar_component_clause,[],[f2265]) ).
fof(f19251,plain,
( spl0_949
| ~ spl0_134
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1818,f1803,f1083,f19249]) ).
fof(f19249,plain,
( spl0_949
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
| subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f1818,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
| subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4) )
| ~ spl0_134
| ~ spl0_202 ),
inference(resolution,[],[f1804,f1084]) ).
fof(f19247,plain,
( spl0_948
| ~ spl0_93
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1137,f1087,f702,f19245]) ).
fof(f19245,plain,
( spl0_948
<=> ! [X4,X0,X3,X2,X1] :
( subclass(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f1137,plain,
( ! [X2,X3,X0,X1,X4] :
( subclass(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_135 ),
inference(resolution,[],[f1088,f703]) ).
fof(f19243,plain,
( spl0_947
| ~ spl0_93
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1119,f1083,f702,f19241]) ).
fof(f19241,plain,
( spl0_947
<=> ! [X4,X0,X3,X2,X1] :
( subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f1119,plain,
( ! [X2,X3,X0,X1,X4] :
( subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_134 ),
inference(resolution,[],[f1084,f703]) ).
fof(f19163,plain,
( spl0_946
| ~ spl0_99
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1729,f1711,f739,f19161]) ).
fof(f19161,plain,
( spl0_946
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f1729,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
| cross_product(X0,X1) = null_class )
| ~ spl0_99
| ~ spl0_198 ),
inference(superposition,[],[f740,f1712]) ).
fof(f18918,plain,
( spl0_945
| ~ spl0_129
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1857,f1812,f1008,f18916]) ).
fof(f18916,plain,
( spl0_945
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),cross_product(universal_class,universal_class))
| null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f1008,plain,
( spl0_129
<=> ! [X0,X1] :
( member(regular(intersection(X0,X1)),X1)
| intersection(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1857,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),cross_product(universal_class,universal_class))
| null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))) )
| ~ spl0_129
| ~ spl0_204 ),
inference(resolution,[],[f1813,f1009]) ).
fof(f1009,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),X1)
| intersection(X0,X1) = null_class )
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1008]) ).
fof(f18914,plain,
( spl0_944
| ~ spl0_128
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1849,f1812,f1004,f18912]) ).
fof(f18912,plain,
( spl0_944
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),cross_product(universal_class,universal_class))
| null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f1004,plain,
( spl0_128
<=> ! [X0,X1] :
( member(regular(intersection(X0,X1)),X0)
| intersection(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1849,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),cross_product(universal_class,universal_class))
| null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) )
| ~ spl0_128
| ~ spl0_204 ),
inference(resolution,[],[f1813,f1005]) ).
fof(f1005,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),X0)
| intersection(X0,X1) = null_class )
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f1004]) ).
fof(f18910,plain,
( spl0_943
| ~ spl0_129
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1831,f1803,f1008,f18908]) ).
fof(f18908,plain,
( spl0_943
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class))
| null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f1831,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class))
| null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) )
| ~ spl0_129
| ~ spl0_202 ),
inference(resolution,[],[f1804,f1009]) ).
fof(f18906,plain,
( spl0_942
| ~ spl0_128
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1823,f1803,f1004,f18904]) ).
fof(f18904,plain,
( spl0_942
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class))
| null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f1823,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class))
| null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) )
| ~ spl0_128
| ~ spl0_202 ),
inference(resolution,[],[f1804,f1005]) ).
fof(f18902,plain,
( spl0_941
| ~ spl0_93
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1050,f1008,f702,f18900]) ).
fof(f18900,plain,
( spl0_941
<=> ! [X0,X3,X2,X1] :
( null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f1050,plain,
( ! [X2,X3,X0,X1] :
( null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_129 ),
inference(resolution,[],[f1009,f703]) ).
fof(f18898,plain,
( spl0_940
| ~ spl0_93
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1034,f1004,f702,f18896]) ).
fof(f18896,plain,
( spl0_940
<=> ! [X0,X3,X2,X1] :
( null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f1034,plain,
( ! [X2,X3,X0,X1] :
( null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_128 ),
inference(resolution,[],[f1005,f703]) ).
fof(f18834,plain,
( spl0_939
| ~ spl0_27
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1843,f1812,f319,f18832]) ).
fof(f18832,plain,
( spl0_939
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),cross_product(universal_class,universal_class))
| subclass(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f1843,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),cross_product(universal_class,universal_class))
| subclass(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) )
| ~ spl0_27
| ~ spl0_204 ),
inference(resolution,[],[f1813,f320]) ).
fof(f18830,plain,
( spl0_938
| ~ spl0_287
| ~ spl0_926 ),
inference(avatar_split_clause,[],[f18459,f18165,f2739,f18827]) ).
fof(f18459,plain,
( subclass(universal_class,complement(null_class))
| ~ spl0_287
| ~ spl0_926 ),
inference(resolution,[],[f18166,f2740]) ).
fof(f18825,plain,
( spl0_937
| ~ spl0_27
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1817,f1803,f319,f18823]) ).
fof(f18823,plain,
( spl0_937
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f1817,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) )
| ~ spl0_27
| ~ spl0_202 ),
inference(resolution,[],[f1804,f320]) ).
fof(f18781,plain,
( spl0_936
| ~ spl0_111
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2084,f2080,f823,f18779]) ).
fof(f18779,plain,
( spl0_936
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f2080,plain,
( spl0_216
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f2084,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),subset_relation) )
| ~ spl0_111
| ~ spl0_216 ),
inference(resolution,[],[f2081,f824]) ).
fof(f2081,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) )
| ~ spl0_216 ),
inference(avatar_component_clause,[],[f2080]) ).
fof(f18719,plain,
( spl0_935
| ~ spl0_23
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1848,f1812,f299,f18717]) ).
fof(f18717,plain,
( spl0_935
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))))))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
| null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f1848,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))))))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
| null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))) )
| ~ spl0_23
| ~ spl0_204 ),
inference(resolution,[],[f1813,f300]) ).
fof(f18715,plain,
( spl0_934
| ~ spl0_23
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1822,f1803,f299,f18713]) ).
fof(f18713,plain,
( spl0_934
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f1822,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_23
| ~ spl0_202 ),
inference(resolution,[],[f1804,f300]) ).
fof(f18576,plain,
( spl0_933
| ~ spl0_96
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1885,f1868,f727,f18574]) ).
fof(f18574,plain,
( spl0_933
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f727,plain,
( spl0_96
<=> ! [X3,X0,X6,X2] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1885,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),X0) )
| ~ spl0_96
| ~ spl0_205 ),
inference(resolution,[],[f1869,f728]) ).
fof(f728,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f727]) ).
fof(f18455,plain,
( spl0_932
| ~ spl0_111
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2071,f2067,f823,f18453]) ).
fof(f18453,plain,
( spl0_932
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f2067,plain,
( spl0_215
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f2071,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),subset_relation) )
| ~ spl0_111
| ~ spl0_215 ),
inference(resolution,[],[f2068,f824]) ).
fof(f2068,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_215 ),
inference(avatar_component_clause,[],[f2067]) ).
fof(f18405,plain,
( spl0_931
| ~ spl0_98
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1728,f1711,f735,f18403]) ).
fof(f18403,plain,
( spl0_931
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f735,plain,
( spl0_98
<=> ! [X3,X0,X6,X2] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1728,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
| cross_product(X0,X1) = null_class )
| ~ spl0_98
| ~ spl0_198 ),
inference(superposition,[],[f736,f1712]) ).
fof(f736,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f735]) ).
fof(f18401,plain,
( spl0_929
| ~ spl0_930
| ~ spl0_99
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1420,f1369,f739,f18398,f18395]) ).
fof(f18395,plain,
( spl0_929
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),X2)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),flip(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f18398,plain,
( spl0_930
<=> subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f1420,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),flip(X2))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),X2) )
| ~ spl0_99
| ~ spl0_165 ),
inference(resolution,[],[f1370,f740]) ).
fof(f18203,plain,
( spl0_928
| ~ spl0_49
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2033,f1998,f448,f18201]) ).
fof(f18201,plain,
( spl0_928
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(X3,X4)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X4)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f448,plain,
( spl0_49
<=> ! [X4,X0,X1] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f2033,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(X3,X4)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X4)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) )
| ~ spl0_49
| ~ spl0_212 ),
inference(resolution,[],[f1999,f449]) ).
fof(f449,plain,
( ! [X0,X1,X4] :
( member(X4,intersection(X0,X1))
| ~ member(X4,X1)
| ~ member(X4,X0) )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f18199,plain,
( spl0_927
| ~ spl0_49
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2010,f1994,f448,f18197]) ).
fof(f18197,plain,
( spl0_927
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(X3,X4)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X4)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f2010,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(X3,X4)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X4)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3) )
| ~ spl0_49
| ~ spl0_211 ),
inference(resolution,[],[f1995,f449]) ).
fof(f18167,plain,
( spl0_926
| ~ spl0_888
| ~ spl0_915 ),
inference(avatar_split_clause,[],[f17877,f17700,f17013,f18165]) ).
fof(f17700,plain,
( spl0_915
<=> null_class = domain_of(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f17877,plain,
( ! [X0] : ~ member(X0,null_class)
| ~ spl0_888
| ~ spl0_915 ),
inference(superposition,[],[f17014,f17702]) ).
fof(f17702,plain,
( null_class = domain_of(null_class)
| ~ spl0_915 ),
inference(avatar_component_clause,[],[f17700]) ).
fof(f18112,plain,
( spl0_925
| ~ spl0_44
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2035,f1998,f424,f18110]) ).
fof(f18110,plain,
( spl0_925
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f424,plain,
( spl0_44
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f2035,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
| ~ spl0_44
| ~ spl0_212 ),
inference(resolution,[],[f1999,f425]) ).
fof(f425,plain,
( ! [X0,X4] :
( member(X4,complement(X0))
| member(X4,X0)
| ~ member(X4,universal_class) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f18108,plain,
( spl0_924
| ~ spl0_44
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2012,f1994,f424,f18106]) ).
fof(f18106,plain,
( spl0_924
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f2012,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
| ~ spl0_44
| ~ spl0_211 ),
inference(resolution,[],[f1995,f425]) ).
fof(f18104,plain,
( spl0_923
| ~ spl0_79
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1625,f1620,f628,f18102]) ).
fof(f18102,plain,
( spl0_923
<=> ! [X2,X0,X1] :
( null_class = X0
| ~ subclass(X0,cross_product(X1,X2))
| ~ member(X0,universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f1620,plain,
( spl0_193
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| null_class = X0
| ~ subclass(X0,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1625,plain,
( ! [X2,X0,X1] :
( null_class = X0
| ~ subclass(X0,cross_product(X1,X2))
| ~ member(X0,universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))))) )
| ~ spl0_79
| ~ spl0_193 ),
inference(resolution,[],[f1621,f629]) ).
fof(f1621,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
| null_class = X0
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) )
| ~ spl0_193 ),
inference(avatar_component_clause,[],[f1620]) ).
fof(f17741,plain,
( spl0_922
| ~ spl0_30
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2029,f1998,f331,f17739]) ).
fof(f17739,plain,
( spl0_922
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f331,plain,
( spl0_30
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f2029,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
| ~ spl0_30
| ~ spl0_212 ),
inference(resolution,[],[f1999,f332]) ).
fof(f332,plain,
( ! [X0,X1] :
( member(X1,unordered_pair(X0,X1))
| ~ member(X1,universal_class) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f17737,plain,
( spl0_921
| ~ spl0_29
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2028,f1998,f327,f17735]) ).
fof(f17735,plain,
( spl0_921
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f327,plain,
( spl0_29
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f2028,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
| ~ spl0_29
| ~ spl0_212 ),
inference(resolution,[],[f1999,f328]) ).
fof(f328,plain,
( ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f17733,plain,
( spl0_920
| ~ spl0_198
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2023,f1994,f1711,f17731]) ).
fof(f17731,plain,
( spl0_920
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))),rotate(X3))
| ~ member(second(regular(cross_product(X0,X1))),universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f2023,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))),rotate(X3))
| ~ member(second(regular(cross_product(X0,X1))),universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
| cross_product(X0,X1) = null_class )
| ~ spl0_198
| ~ spl0_211 ),
inference(superposition,[],[f1995,f1712]) ).
fof(f17729,plain,
( spl0_919
| ~ spl0_30
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2006,f1994,f331,f17727]) ).
fof(f17727,plain,
( spl0_919
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f2006,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
| ~ spl0_30
| ~ spl0_211 ),
inference(resolution,[],[f1995,f332]) ).
fof(f17725,plain,
( spl0_918
| ~ spl0_29
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2005,f1994,f327,f17723]) ).
fof(f17723,plain,
( spl0_918
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f2005,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
| ~ spl0_29
| ~ spl0_211 ),
inference(resolution,[],[f1995,f328]) ).
fof(f17721,plain,
( spl0_917
| ~ spl0_158
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1768,f1745,f1294,f17719]) ).
fof(f17719,plain,
( spl0_917
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class))))
| ~ operation(X2)
| null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f1768,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class))))
| ~ operation(X2)
| null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class) )
| ~ spl0_158
| ~ spl0_199 ),
inference(resolution,[],[f1746,f1295]) ).
fof(f17717,plain,
( spl0_916
| ~ spl0_96
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1727,f1711,f727,f17715]) ).
fof(f17715,plain,
( spl0_916
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f1727,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
| cross_product(X0,X1) = null_class )
| ~ spl0_96
| ~ spl0_198 ),
inference(superposition,[],[f728,f1712]) ).
fof(f17703,plain,
( spl0_915
| ~ spl0_23
| ~ spl0_888 ),
inference(avatar_split_clause,[],[f17110,f17013,f299,f17700]) ).
fof(f17670,plain,
( spl0_914
| ~ spl0_786
| ~ spl0_869
| ~ spl0_913 ),
inference(avatar_split_clause,[],[f17666,f17658,f16536,f14703,f17668]) ).
fof(f17668,plain,
( spl0_914
<=> ! [X2,X0,X1] :
( subclass(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f17658,plain,
( spl0_913
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
| null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f17666,plain,
( ! [X2,X0,X1] :
( subclass(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_786
| ~ spl0_869
| ~ spl0_913 ),
inference(forward_demodulation,[],[f17665,f16537]) ).
fof(f17665,plain,
( ! [X2,X0,X1] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))),X2)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_786
| ~ spl0_869
| ~ spl0_913 ),
inference(forward_demodulation,[],[f17664,f14705]) ).
fof(f17664,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_786
| ~ spl0_869
| ~ spl0_913 ),
inference(forward_demodulation,[],[f17663,f16537]) ).
fof(f17663,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_786
| ~ spl0_869
| ~ spl0_913 ),
inference(forward_demodulation,[],[f17662,f14705]) ).
fof(f17662,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_786
| ~ spl0_869
| ~ spl0_913 ),
inference(forward_demodulation,[],[f17661,f16537]) ).
fof(f17661,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_786
| ~ spl0_913 ),
inference(forward_demodulation,[],[f17659,f14705]) ).
fof(f17659,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_913 ),
inference(avatar_component_clause,[],[f17658]) ).
fof(f17660,plain,
( spl0_913
| ~ spl0_40
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2087,f2080,f380,f17658]) ).
fof(f2087,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_40
| ~ spl0_216 ),
inference(superposition,[],[f2081,f381]) ).
fof(f17656,plain,
( spl0_912
| ~ spl0_193
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1854,f1812,f1620,f17654]) ).
fof(f17654,plain,
( spl0_912
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| null_class = X1
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f1854,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| null_class = X1
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class) )
| ~ spl0_193
| ~ spl0_204 ),
inference(resolution,[],[f1813,f1621]) ).
fof(f17652,plain,
( spl0_911
| ~ spl0_193
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1828,f1803,f1620,f17650]) ).
fof(f17650,plain,
( spl0_911
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| null_class = X1
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f1828,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| null_class = X1
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X1,universal_class) )
| ~ spl0_193
| ~ spl0_202 ),
inference(resolution,[],[f1804,f1621]) ).
fof(f17648,plain,
( spl0_910
| ~ spl0_93
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1632,f1620,f702,f17646]) ).
fof(f17646,plain,
( spl0_910
<=> ! [X0,X3,X2,X1] :
( null_class = X0
| ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f1632,plain,
( ! [X2,X3,X0,X1] :
( null_class = X0
| ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_193 ),
inference(resolution,[],[f1621,f703]) ).
fof(f17636,plain,
( spl0_909
| spl0_853
| ~ spl0_786
| ~ spl0_869
| ~ spl0_907 ),
inference(avatar_split_clause,[],[f17627,f17619,f16536,f14703,f16040,f17634]) ).
fof(f17634,plain,
( spl0_909
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f16040,plain,
( spl0_853
<=> null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f17619,plain,
( spl0_907
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f17627,plain,
( ! [X0,X1] :
( null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_786
| ~ spl0_869
| ~ spl0_907 ),
inference(forward_demodulation,[],[f17626,f16537]) ).
fof(f17626,plain,
( ! [X0,X1] :
( null_class = domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_786
| ~ spl0_869
| ~ spl0_907 ),
inference(forward_demodulation,[],[f17625,f14705]) ).
fof(f17625,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class))
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_786
| ~ spl0_869
| ~ spl0_907 ),
inference(forward_demodulation,[],[f17624,f16537]) ).
fof(f17624,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class))
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_786
| ~ spl0_869
| ~ spl0_907 ),
inference(forward_demodulation,[],[f17623,f14705]) ).
fof(f17623,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_786
| ~ spl0_869
| ~ spl0_907 ),
inference(forward_demodulation,[],[f17622,f16537]) ).
fof(f17622,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_786
| ~ spl0_907 ),
inference(forward_demodulation,[],[f17620,f14705]) ).
fof(f17620,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_907 ),
inference(avatar_component_clause,[],[f17619]) ).
fof(f17631,plain,
( spl0_908
| ~ spl0_27
| ~ spl0_888 ),
inference(avatar_split_clause,[],[f17102,f17013,f319,f17629]) ).
fof(f17629,plain,
( spl0_908
<=> ! [X0] : subclass(domain_of(null_class),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f17102,plain,
( ! [X0] : subclass(domain_of(null_class),X0)
| ~ spl0_27
| ~ spl0_888 ),
inference(resolution,[],[f17014,f320]) ).
fof(f17621,plain,
( spl0_907
| ~ spl0_40
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2074,f2067,f380,f17619]) ).
fof(f2074,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_40
| ~ spl0_215 ),
inference(superposition,[],[f2068,f381]) ).
fof(f17604,plain,
( spl0_906
| ~ spl0_24
| ~ spl0_100
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1874,f1868,f745,f303,f17602]) ).
fof(f17602,plain,
( spl0_906
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f303,plain,
( spl0_24
<=> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f1874,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,domain_of(X0))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function) )
| ~ spl0_100
| ~ spl0_205 ),
inference(resolution,[],[f1869,f746]) ).
fof(f17576,plain,
( spl0_905
| ~ spl0_111
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2060,f2051,f823,f17574]) ).
fof(f17574,plain,
( spl0_905
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(X1,domain_of(X0))
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f2060,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(X1,domain_of(X0))
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),subset_relation) )
| ~ spl0_111
| ~ spl0_213 ),
inference(resolution,[],[f2052,f824]) ).
fof(f17533,plain,
( spl0_904
| ~ spl0_77
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2083,f2080,f613,f17531]) ).
fof(f17531,plain,
( spl0_904
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| ~ member(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f2083,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| ~ member(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_77
| ~ spl0_216 ),
inference(resolution,[],[f2081,f614]) ).
fof(f17392,plain,
( spl0_903
| ~ spl0_77
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2070,f2067,f613,f17390]) ).
fof(f17390,plain,
( spl0_903
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
| ~ member(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f2070,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
| ~ member(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_77
| ~ spl0_215 ),
inference(resolution,[],[f2068,f614]) ).
fof(f17387,plain,
( ~ spl0_902
| ~ spl0_12
| ~ spl0_888 ),
inference(avatar_split_clause,[],[f17106,f17013,f254,f17384]) ).
fof(f17384,plain,
( spl0_902
<=> inductive(domain_of(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f254,plain,
( spl0_12
<=> ! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f17106,plain,
( ~ inductive(domain_of(null_class))
| ~ spl0_12
| ~ spl0_888 ),
inference(resolution,[],[f17014,f255]) ).
fof(f255,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f17382,plain,
( spl0_901
| ~ spl0_95
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1726,f1711,f723,f17380]) ).
fof(f17380,plain,
( spl0_901
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f1726,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
| cross_product(X0,X1) = null_class )
| ~ spl0_95
| ~ spl0_198 ),
inference(superposition,[],[f724,f1712]) ).
fof(f17235,plain,
( spl0_652
| spl0_900
| ~ spl0_77
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2059,f2051,f613,f17233,f9911]) ).
fof(f17233,plain,
( spl0_900
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| ~ member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f2059,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(X1,domain_of(X0))
| ~ member(X0,universal_class)
| ~ member(X2,universal_class)
| ~ member(X1,universal_class) )
| ~ spl0_77
| ~ spl0_213 ),
inference(resolution,[],[f2052,f614]) ).
fof(f17231,plain,
( spl0_899
| ~ spl0_95
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1418,f1369,f723,f17229]) ).
fof(f17229,plain,
( spl0_899
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,rotate(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(X1,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f1418,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,rotate(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(X1,X1))),X0) )
| ~ spl0_95
| ~ spl0_165 ),
inference(resolution,[],[f1370,f724]) ).
fof(f17227,plain,
( ~ spl0_897
| spl0_898
| ~ spl0_90
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1205,f1167,f686,f17225,f17221]) ).
fof(f17221,plain,
( spl0_897
<=> operation(flip(cross_product(subset_relation,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f17225,plain,
( spl0_898
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1)),unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),unordered_pair(not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1)))),subset_relation)
| homomorphism(X0,flip(cross_product(subset_relation,universal_class)),X1)
| ~ compatible(X0,flip(cross_product(subset_relation,universal_class)),X1)
| ~ operation(X1)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1)),unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),unordered_pair(not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f1205,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1)),unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),unordered_pair(not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1)))),subset_relation)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1)),unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),unordered_pair(not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1)))),identity_relation)
| ~ operation(X1)
| ~ compatible(X0,flip(cross_product(subset_relation,universal_class)),X1)
| homomorphism(X0,flip(cross_product(subset_relation,universal_class)),X1)
| ~ operation(flip(cross_product(subset_relation,universal_class))) )
| ~ spl0_90
| ~ spl0_144 ),
inference(resolution,[],[f1168,f687]) ).
fof(f17219,plain,
( spl0_895
| ~ spl0_896
| ~ spl0_100
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f838,f802,f745,f17216,f17213]) ).
fof(f17213,plain,
( spl0_895
<=> ! [X0,X1] :
( ~ member(X0,domain_of(X1))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f17216,plain,
( spl0_896
<=> subclass(universal_class,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f838,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ member(X0,domain_of(X1))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function) )
| ~ spl0_100
| ~ spl0_106 ),
inference(resolution,[],[f803,f746]) ).
fof(f17099,plain,
( spl0_893
| ~ spl0_894
| ~ spl0_185
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1893,f1868,f1556,f17096,f17093]) ).
fof(f17093,plain,
( spl0_893
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f17096,plain,
( spl0_894
<=> subclass(composition_function,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f1893,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_185
| ~ spl0_205 ),
inference(resolution,[],[f1869,f1557]) ).
fof(f17046,plain,
( spl0_892
| ~ spl0_162
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2034,f1998,f1351,f17044]) ).
fof(f17044,plain,
( spl0_892
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f1351,plain,
( spl0_162
<=> ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f2034,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
| ~ spl0_162
| ~ spl0_212 ),
inference(resolution,[],[f1999,f1352]) ).
fof(f1352,plain,
( ! [X0] :
( member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,subset_relation) )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1351]) ).
fof(f17042,plain,
( spl0_891
| ~ spl0_162
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2011,f1994,f1351,f17040]) ).
fof(f17040,plain,
( spl0_891
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f2011,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
| ~ spl0_162
| ~ spl0_211 ),
inference(resolution,[],[f1995,f1352]) ).
fof(f17023,plain,
( spl0_890
| ~ spl0_171
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1852,f1812,f1456,f17021]) ).
fof(f17021,plain,
( spl0_890
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f1456,plain,
( spl0_171
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(universal_class,X1)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f1852,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class) )
| ~ spl0_171
| ~ spl0_204 ),
inference(resolution,[],[f1813,f1457]) ).
fof(f1457,plain,
( ! [X0,X1] :
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,universal_class) )
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f1456]) ).
fof(f17019,plain,
( spl0_889
| ~ spl0_171
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1826,f1803,f1456,f17017]) ).
fof(f17017,plain,
( spl0_889
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f1826,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X1,universal_class) )
| ~ spl0_171
| ~ spl0_202 ),
inference(resolution,[],[f1804,f1457]) ).
fof(f17015,plain,
( spl0_888
| ~ spl0_145
| ~ spl0_869 ),
inference(avatar_split_clause,[],[f16859,f16536,f1171,f17013]) ).
fof(f1171,plain,
( spl0_145
<=> ! [X0,X1] :
( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,domain_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f16859,plain,
( ! [X0] : ~ member(X0,domain_of(null_class))
| ~ spl0_145
| ~ spl0_869 ),
inference(trivial_inequality_removal,[],[f16811]) ).
fof(f16811,plain,
( ! [X0] :
( null_class != null_class
| ~ member(X0,domain_of(null_class)) )
| ~ spl0_145
| ~ spl0_869 ),
inference(superposition,[],[f1172,f16537]) ).
fof(f1172,plain,
( ! [X0,X1] :
( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,domain_of(X1)) )
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f1171]) ).
fof(f17011,plain,
( spl0_887
| ~ spl0_93
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1506,f1456,f702,f17009]) ).
fof(f17009,plain,
( spl0_887
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X3,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f1506,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X3,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_171 ),
inference(resolution,[],[f1457,f703]) ).
fof(f16970,plain,
( spl0_886
| ~ spl0_186
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2047,f1998,f1578,f16968]) ).
fof(f16968,plain,
( spl0_886
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(compose_class(X2)))
| ~ member(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f2047,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(compose_class(X2)))
| ~ member(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
| ~ spl0_186
| ~ spl0_212 ),
inference(duplicate_literal_removal,[],[f2043]) ).
fof(f2043,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(compose_class(X2)))
| ~ member(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
| ~ spl0_186
| ~ spl0_212 ),
inference(resolution,[],[f1999,f1579]) ).
fof(f16925,plain,
( spl0_885
| ~ spl0_165
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2024,f1998,f1369,f16923]) ).
fof(f16923,plain,
( spl0_885
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(X2))
| ~ member(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(domain_relation,X2)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f2024,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(X2))
| ~ member(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(domain_relation,X2)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
| ~ spl0_165
| ~ spl0_212 ),
inference(resolution,[],[f1999,f1370]) ).
fof(f16736,plain,
( spl0_884
| ~ spl0_40
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2090,f2080,f380,f16734]) ).
fof(f16734,plain,
( spl0_884
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
| subclass(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f2090,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
| subclass(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
| ~ spl0_40
| ~ spl0_216 ),
inference(superposition,[],[f2081,f381]) ).
fof(f16732,plain,
( spl0_883
| ~ spl0_199
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1931,f1923,f1745,f16730]) ).
fof(f16730,plain,
( spl0_883
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),compose(X3,X4))
| ~ member(not_homomorphism2(X0,X1,X2),universal_class)
| null_class = intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))
| ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
| ~ operation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f1923,plain,
( spl0_208
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class)
| null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f1931,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),compose(X3,X4))
| ~ member(not_homomorphism2(X0,X1,X2),universal_class)
| null_class = intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))
| ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
| ~ operation(X2) )
| ~ spl0_199
| ~ spl0_208 ),
inference(resolution,[],[f1924,f1746]) ).
fof(f1924,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X1,universal_class)
| null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_208 ),
inference(avatar_component_clause,[],[f1923]) ).
fof(f16728,plain,
( spl0_882
| ~ spl0_165
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1851,f1812,f1369,f16726]) ).
fof(f16726,plain,
( spl0_882
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),cross_product(universal_class,universal_class))
| ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f1851,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),cross_product(universal_class,universal_class))
| ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class) )
| ~ spl0_165
| ~ spl0_204 ),
inference(resolution,[],[f1813,f1370]) ).
fof(f16724,plain,
( spl0_881
| ~ spl0_165
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1825,f1803,f1369,f16722]) ).
fof(f16722,plain,
( spl0_881
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),cross_product(universal_class,universal_class))
| ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f1825,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),cross_product(universal_class,universal_class))
| ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X1,universal_class) )
| ~ spl0_165
| ~ spl0_202 ),
inference(resolution,[],[f1804,f1370]) ).
fof(f16720,plain,
( spl0_880
| ~ spl0_93
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1430,f1369,f702,f16718]) ).
fof(f16718,plain,
( spl0_880
<=> ! [X0,X3,X2,X1] :
( ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X3,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f1430,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X3,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_165 ),
inference(resolution,[],[f1370,f703]) ).
fof(f16602,plain,
( spl0_879
| ~ spl0_224
| ~ spl0_836 ),
inference(avatar_split_clause,[],[f16387,f15770,f2227,f16600]) ).
fof(f16600,plain,
( spl0_879
<=> ! [X0] : null_class = intersection(X0,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f15770,plain,
( spl0_836
<=> ! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f16387,plain,
( ! [X0] : null_class = intersection(X0,null_class)
| ~ spl0_224
| ~ spl0_836 ),
inference(resolution,[],[f15771,f2228]) ).
fof(f15771,plain,
( ! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 )
| ~ spl0_836 ),
inference(avatar_component_clause,[],[f15770]) ).
fof(f16598,plain,
( spl0_878
| ~ spl0_235
| ~ spl0_873 ),
inference(avatar_split_clause,[],[f16557,f16554,f2310,f16596]) ).
fof(f16596,plain,
( spl0_878
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f16554,plain,
( spl0_873
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f16557,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_235
| ~ spl0_873 ),
inference(forward_demodulation,[],[f16555,f2312]) ).
fof(f16555,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),identity_relation) )
| ~ spl0_873 ),
inference(avatar_component_clause,[],[f16554]) ).
fof(f16594,plain,
( spl0_877
| ~ spl0_235
| ~ spl0_872 ),
inference(avatar_split_clause,[],[f16552,f16549,f2310,f16592]) ).
fof(f16592,plain,
( spl0_877
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(compose(element_relation,complement(singleton_relation)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f16549,plain,
( spl0_872
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(compose(element_relation,complement(identity_relation)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f16552,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(compose(element_relation,complement(singleton_relation)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation) )
| ~ spl0_235
| ~ spl0_872 ),
inference(forward_demodulation,[],[f16550,f2312]) ).
fof(f16550,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(compose(element_relation,complement(identity_relation)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation) )
| ~ spl0_872 ),
inference(avatar_component_clause,[],[f16549]) ).
fof(f16569,plain,
( spl0_876
| ~ spl0_235
| ~ spl0_870 ),
inference(avatar_split_clause,[],[f16543,f16540,f2310,f16567]) ).
fof(f16567,plain,
( spl0_876
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f16540,plain,
( spl0_870
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f16543,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_235
| ~ spl0_870 ),
inference(forward_demodulation,[],[f16541,f2312]) ).
fof(f16541,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),identity_relation) )
| ~ spl0_870 ),
inference(avatar_component_clause,[],[f16540]) ).
fof(f16565,plain,
( spl0_875
| ~ spl0_235
| ~ spl0_868 ),
inference(avatar_split_clause,[],[f16534,f16531,f2310,f16563]) ).
fof(f16563,plain,
( spl0_875
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(compose(element_relation,complement(singleton_relation)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f16531,plain,
( spl0_868
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(compose(element_relation,complement(identity_relation)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f16534,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(compose(element_relation,complement(singleton_relation)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation) )
| ~ spl0_235
| ~ spl0_868 ),
inference(forward_demodulation,[],[f16532,f2312]) ).
fof(f16532,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(compose(element_relation,complement(identity_relation)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation) )
| ~ spl0_868 ),
inference(avatar_component_clause,[],[f16531]) ).
fof(f16561,plain,
( spl0_874
| ~ spl0_123
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2042,f1998,f951,f16559]) ).
fof(f16559,plain,
( spl0_874
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(regular(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),null_class)
| null_class = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f951,plain,
( spl0_123
<=> ! [X0,X1] :
( ~ member(X1,null_class)
| member(X1,regular(X0))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f2042,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(regular(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),null_class)
| null_class = X3 )
| ~ spl0_123
| ~ spl0_212 ),
inference(resolution,[],[f1999,f952]) ).
fof(f952,plain,
( ! [X0,X1] :
( member(X1,regular(X0))
| ~ member(X1,null_class)
| null_class = X0 )
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f951]) ).
fof(f16556,plain,
( spl0_873
| ~ spl0_125
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2038,f1998,f959,f16554]) ).
fof(f2038,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),identity_relation) )
| ~ spl0_125
| ~ spl0_212 ),
inference(resolution,[],[f1999,f960]) ).
fof(f16551,plain,
( spl0_872
| ~ spl0_124
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2036,f1998,f955,f16549]) ).
fof(f2036,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(compose(element_relation,complement(identity_relation)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation) )
| ~ spl0_124
| ~ spl0_212 ),
inference(resolution,[],[f1999,f956]) ).
fof(f16547,plain,
( spl0_871
| ~ spl0_123
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2019,f1994,f951,f16545]) ).
fof(f16545,plain,
( spl0_871
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(regular(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),null_class)
| null_class = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f2019,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(regular(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),null_class)
| null_class = X3 )
| ~ spl0_123
| ~ spl0_211 ),
inference(resolution,[],[f1995,f952]) ).
fof(f16542,plain,
( spl0_870
| ~ spl0_125
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2015,f1994,f959,f16540]) ).
fof(f2015,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),identity_relation) )
| ~ spl0_125
| ~ spl0_211 ),
inference(resolution,[],[f1995,f960]) ).
fof(f16538,plain,
( spl0_869
| ~ spl0_223
| ~ spl0_836 ),
inference(avatar_split_clause,[],[f16386,f15770,f2223,f16536]) ).
fof(f16386,plain,
( ! [X0] : null_class = intersection(null_class,X0)
| ~ spl0_223
| ~ spl0_836 ),
inference(resolution,[],[f15771,f2224]) ).
fof(f16533,plain,
( spl0_868
| ~ spl0_124
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2013,f1994,f955,f16531]) ).
fof(f2013,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(compose(element_relation,complement(identity_relation)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation) )
| ~ spl0_124
| ~ spl0_211 ),
inference(resolution,[],[f1995,f956]) ).
fof(f16412,plain,
( spl0_867
| ~ spl0_66
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2045,f1998,f552,f16410]) ).
fof(f16410,plain,
( spl0_867
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(domain_relation))
| ~ member(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f2045,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(domain_relation))
| ~ member(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
| ~ spl0_66
| ~ spl0_212 ),
inference(resolution,[],[f1999,f553]) ).
fof(f16408,plain,
( spl0_866
| ~ spl0_142
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1903,f1868,f1159,f16406]) ).
fof(f16406,plain,
( spl0_866
<=> ! [X2,X0,X1] :
( ~ subclass(composition_function,regular(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),null_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f1159,plain,
( spl0_142
<=> ! [X0,X1] :
( member(X1,null_class)
| ~ member(X1,regular(X0))
| ~ member(X1,X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1903,plain,
( ! [X2,X0,X1] :
( ~ subclass(composition_function,regular(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),null_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0)
| null_class = X0 )
| ~ spl0_142
| ~ spl0_205 ),
inference(resolution,[],[f1869,f1160]) ).
fof(f1160,plain,
( ! [X0,X1] :
( ~ member(X1,regular(X0))
| member(X1,null_class)
| ~ member(X1,X0)
| null_class = X0 )
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f16403,plain,
( spl0_864
| ~ spl0_865
| ~ spl0_144
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1900,f1868,f1167,f16400,f16397]) ).
fof(f16397,plain,
( spl0_864
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),identity_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f16400,plain,
( spl0_865
<=> subclass(composition_function,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f1900,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),identity_relation) )
| ~ spl0_144
| ~ spl0_205 ),
inference(resolution,[],[f1869,f1168]) ).
fof(f16382,plain,
( ~ spl0_863
| ~ spl0_235
| spl0_862 ),
inference(avatar_split_clause,[],[f16377,f16373,f2310,f16379]) ).
fof(f16379,plain,
( spl0_863
<=> subclass(composition_function,complement(compose(element_relation,complement(singleton_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f16373,plain,
( spl0_862
<=> subclass(composition_function,complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f16377,plain,
( ~ subclass(composition_function,complement(compose(element_relation,complement(singleton_relation))))
| ~ spl0_235
| spl0_862 ),
inference(forward_demodulation,[],[f16375,f2312]) ).
fof(f16375,plain,
( ~ subclass(composition_function,complement(compose(element_relation,complement(identity_relation))))
| spl0_862 ),
inference(avatar_component_clause,[],[f16373]) ).
fof(f16376,plain,
( spl0_861
| ~ spl0_862
| ~ spl0_143
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1895,f1868,f1163,f16373,f16370]) ).
fof(f16370,plain,
( spl0_861
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),singleton_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f1163,plain,
( spl0_143
<=> ! [X0] :
( member(X0,singleton_relation)
| ~ member(X0,element_relation)
| ~ member(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1895,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,complement(compose(element_relation,complement(identity_relation))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),singleton_relation) )
| ~ spl0_143
| ~ spl0_205 ),
inference(resolution,[],[f1869,f1164]) ).
fof(f1164,plain,
( ! [X0] :
( ~ member(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,element_relation)
| member(X0,singleton_relation) )
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1163]) ).
fof(f16368,plain,
( spl0_860
| ~ spl0_170
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1860,f1812,f1452,f16366]) ).
fof(f16366,plain,
( spl0_860
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
| ~ function(X2)
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f1452,plain,
( spl0_170
<=> ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ function(X1)
| ~ subclass(universal_class,X2)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1860,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
| ~ function(X2)
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class) )
| ~ spl0_170
| ~ spl0_204 ),
inference(resolution,[],[f1813,f1453]) ).
fof(f1453,plain,
( ! [X2,X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2)
| ~ function(X1)
| ~ subclass(universal_class,X2)
| ~ member(X0,universal_class) )
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1452]) ).
fof(f16364,plain,
( spl0_859
| ~ spl0_170
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1834,f1803,f1452,f16362]) ).
fof(f16362,plain,
( spl0_859
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
| ~ function(X2)
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f1834,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
| ~ function(X2)
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(X1,universal_class) )
| ~ spl0_170
| ~ spl0_202 ),
inference(resolution,[],[f1804,f1453]) ).
fof(f16301,plain,
( spl0_858
| spl0_631
| ~ spl0_79
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1500,f1456,f628,f9581,f16299]) ).
fof(f16299,plain,
( spl0_858
<=> ! [X2] :
( ~ member(X2,universal_class)
| complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = unordered_pair(unordered_pair(first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))))),unordered_pair(first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),unordered_pair(second(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),second(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f9581,plain,
( spl0_631
<=> ! [X0,X1] : ~ subclass(universal_class,cross_product(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f1500,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| ~ member(X2,universal_class)
| complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = unordered_pair(unordered_pair(first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))))),unordered_pair(first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),unordered_pair(second(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),second(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))))))) )
| ~ spl0_79
| ~ spl0_171 ),
inference(resolution,[],[f1457,f629]) ).
fof(f16297,plain,
( spl0_857
| ~ spl0_93
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1488,f1452,f702,f16295]) ).
fof(f16295,plain,
( spl0_857
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(X4,universal_class)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f1488,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(X4,universal_class)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_170 ),
inference(resolution,[],[f1453,f703]) ).
fof(f16280,plain,
( ~ spl0_80
| spl0_179
| ~ spl0_853 ),
inference(avatar_split_clause,[],[f16050,f16040,f1522,f636]) ).
fof(f636,plain,
( spl0_80
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1522,plain,
( spl0_179
<=> member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f16050,plain,
( ~ member(null_class,universal_class)
| spl0_179
| ~ spl0_853 ),
inference(superposition,[],[f1523,f16042]) ).
fof(f16042,plain,
( null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class))))
| ~ spl0_853 ),
inference(avatar_component_clause,[],[f16040]) ).
fof(f1523,plain,
( ~ member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
| spl0_179 ),
inference(avatar_component_clause,[],[f1522]) ).
fof(f16234,plain,
( spl0_856
| ~ spl0_111
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2031,f1998,f823,f16232]) ).
fof(f16232,plain,
( spl0_856
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(universal_class,universal_class)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f2031,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(universal_class,universal_class)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
| ~ spl0_111
| ~ spl0_212 ),
inference(resolution,[],[f1999,f824]) ).
fof(f16230,plain,
( spl0_855
| ~ spl0_111
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2008,f1994,f823,f16228]) ).
fof(f16228,plain,
( spl0_855
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(universal_class,universal_class)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f2008,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(universal_class,universal_class)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
| ~ spl0_111
| ~ spl0_211 ),
inference(resolution,[],[f1995,f824]) ).
fof(f16046,plain,
( spl0_853
| spl0_854
| ~ spl0_40
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2077,f2067,f380,f16044,f16040]) ).
fof(f16044,plain,
( spl0_854
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f2077,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
| null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class))))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
| ~ spl0_40
| ~ spl0_215 ),
inference(superposition,[],[f2068,f381]) ).
fof(f16038,plain,
( spl0_852
| ~ spl0_48
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1889,f1868,f444,f16036]) ).
fof(f16036,plain,
( spl0_852
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))) = X0
| unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f444,plain,
( spl0_48
<=> ! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f1889,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))) = X0
| unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))) = X1 )
| ~ spl0_48
| ~ spl0_205 ),
inference(resolution,[],[f1869,f445]) ).
fof(f445,plain,
( ! [X2,X0,X1] :
( ~ member(X2,unordered_pair(X0,X1))
| X0 = X2
| X1 = X2 )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f16017,plain,
( spl0_851
| ~ spl0_158
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1634,f1620,f1294,f16015]) ).
fof(f16015,plain,
( spl0_851
<=> ! [X0] :
( null_class = X0
| ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class))))
| ~ member(X0,universal_class)
| null_class = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f1634,plain,
( ! [X0] :
( null_class = X0
| ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class))))
| ~ member(X0,universal_class)
| null_class = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class) )
| ~ spl0_158
| ~ spl0_193 ),
inference(resolution,[],[f1621,f1295]) ).
fof(f16013,plain,
( spl0_850
| ~ spl0_32
| ~ spl0_603 ),
inference(avatar_split_clause,[],[f11993,f9139,f339,f16011]) ).
fof(f16011,plain,
( spl0_850
<=> ! [X0,X1] :
( ~ member(X1,null_class)
| member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f339,plain,
( spl0_32
<=> ! [X4,X0,X1] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f9139,plain,
( spl0_603
<=> ! [X0] : null_class = intersection(complement(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f11993,plain,
( ! [X0,X1] :
( ~ member(X1,null_class)
| member(X1,X0) )
| ~ spl0_32
| ~ spl0_603 ),
inference(superposition,[],[f340,f9140]) ).
fof(f9140,plain,
( ! [X0] : null_class = intersection(complement(X0),X0)
| ~ spl0_603 ),
inference(avatar_component_clause,[],[f9139]) ).
fof(f340,plain,
( ! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X1) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f15997,plain,
( spl0_849
| ~ spl0_185
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1762,f1745,f1556,f15995]) ).
fof(f15995,plain,
( spl0_849
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f1762,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),cross_product(universal_class,universal_class)) )
| ~ spl0_185
| ~ spl0_199 ),
inference(resolution,[],[f1746,f1557]) ).
fof(f15993,plain,
( spl0_848
| ~ spl0_50
| ~ spl0_70
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f1654,f1639,f568,f452,f15991]) ).
fof(f15991,plain,
( spl0_848
<=> ! [X0] :
( null_class = intersection(X0,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class)))))))),universal_class))
| null_class = complement(domain_of(X0))
| ~ member(complement(domain_of(X0)),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f1639,plain,
( spl0_194
<=> ! [X0] :
( ~ member(complement(X0),universal_class)
| complement(X0) = null_class
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f1654,plain,
( ! [X0] :
( null_class = intersection(X0,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class)))))))),universal_class))
| null_class = complement(domain_of(X0))
| ~ member(complement(domain_of(X0)),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class) )
| ~ spl0_50
| ~ spl0_70
| ~ spl0_194 ),
inference(forward_demodulation,[],[f1650,f453]) ).
fof(f1650,plain,
( ! [X0] :
( null_class = complement(domain_of(X0))
| ~ member(complement(domain_of(X0)),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class)
| null_class = intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class)))))))),universal_class),X0) )
| ~ spl0_70
| ~ spl0_194 ),
inference(resolution,[],[f1640,f569]) ).
fof(f1640,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0)
| complement(X0) = null_class
| ~ member(complement(X0),universal_class) )
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f1639]) ).
fof(f15897,plain,
( spl0_847
| ~ spl0_235
| ~ spl0_842 ),
inference(avatar_split_clause,[],[f15877,f15874,f2310,f15895]) ).
fof(f15895,plain,
( spl0_847
<=> ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),singleton_relation)
| null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
| ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f15874,plain,
( spl0_842
<=> ! [X0] :
( null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
| ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f15877,plain,
( ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),singleton_relation)
| null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
| ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_235
| ~ spl0_842 ),
inference(forward_demodulation,[],[f15875,f2312]) ).
fof(f15875,plain,
( ! [X0] :
( null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
| ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),identity_relation) )
| ~ spl0_842 ),
inference(avatar_component_clause,[],[f15874]) ).
fof(f15893,plain,
( spl0_846
| ~ spl0_235
| ~ spl0_841 ),
inference(avatar_split_clause,[],[f15872,f15866,f2310,f15891]) ).
fof(f15891,plain,
( spl0_846
<=> ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),intersection(complement(compose(element_relation,complement(singleton_relation))),X0)),universal_class)),universal_class))))))),singleton_relation)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),intersection(complement(compose(element_relation,complement(singleton_relation))),X0)),universal_class)),universal_class))))))),element_relation)
| ~ member(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),universal_class)
| null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f15866,plain,
( spl0_841
<=> ! [X0] :
( null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0)
| ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f15872,plain,
( ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),intersection(complement(compose(element_relation,complement(singleton_relation))),X0)),universal_class)),universal_class))))))),singleton_relation)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),intersection(complement(compose(element_relation,complement(singleton_relation))),X0)),universal_class)),universal_class))))))),element_relation)
| ~ member(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),universal_class)
| null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),X0) )
| ~ spl0_235
| ~ spl0_841 ),
inference(forward_demodulation,[],[f15871,f2312]) ).
fof(f15871,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),intersection(complement(compose(element_relation,complement(singleton_relation))),X0)),universal_class)),universal_class))))))),element_relation)
| ~ member(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),universal_class)
| null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),X0)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
| ~ spl0_235
| ~ spl0_841 ),
inference(forward_demodulation,[],[f15870,f2312]) ).
fof(f15870,plain,
( ! [X0] :
( ~ member(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),universal_class)
| null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),X0)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
| ~ spl0_235
| ~ spl0_841 ),
inference(forward_demodulation,[],[f15869,f2312]) ).
fof(f15869,plain,
( ! [X0] :
( null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),X0)
| ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
| ~ spl0_235
| ~ spl0_841 ),
inference(forward_demodulation,[],[f15867,f2312]) ).
fof(f15867,plain,
( ! [X0] :
( null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0)
| ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
| ~ spl0_841 ),
inference(avatar_component_clause,[],[f15866]) ).
fof(f15889,plain,
( spl0_845
| ~ spl0_20
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f3598,f3477,f287,f15887]) ).
fof(f15887,plain,
( spl0_845
<=> ! [X0] :
( ~ member(X0,null_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f3477,plain,
( spl0_341
<=> null_class = complement(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f3598,plain,
( ! [X0] :
( ~ member(X0,null_class)
| ~ member(X0,universal_class) )
| ~ spl0_20
| ~ spl0_341 ),
inference(superposition,[],[f288,f3479]) ).
fof(f3479,plain,
( null_class = complement(universal_class)
| ~ spl0_341 ),
inference(avatar_component_clause,[],[f3477]) ).
fof(f15885,plain,
( spl0_844
| ~ spl0_235
| ~ spl0_840 ),
inference(avatar_split_clause,[],[f15864,f15861,f2310,f15883]) ).
fof(f15883,plain,
( spl0_844
<=> ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),singleton_relation)
| null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f15861,plain,
( spl0_840
<=> ! [X0] :
( null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f15864,plain,
( ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),singleton_relation)
| null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_235
| ~ spl0_840 ),
inference(forward_demodulation,[],[f15862,f2312]) ).
fof(f15862,plain,
( ! [X0] :
( null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation) )
| ~ spl0_840 ),
inference(avatar_component_clause,[],[f15861]) ).
fof(f15881,plain,
( spl0_843
| ~ spl0_235
| ~ spl0_839 ),
inference(avatar_split_clause,[],[f15859,f15853,f2310,f15879]) ).
fof(f15879,plain,
( spl0_843
<=> ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),singleton_relation)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),element_relation)
| ~ member(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),universal_class)
| null_class = intersection(X0,complement(compose(element_relation,complement(singleton_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f15853,plain,
( spl0_839
<=> ! [X0] :
( null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f15859,plain,
( ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),singleton_relation)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),element_relation)
| ~ member(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),universal_class)
| null_class = intersection(X0,complement(compose(element_relation,complement(singleton_relation)))) )
| ~ spl0_235
| ~ spl0_839 ),
inference(forward_demodulation,[],[f15858,f2312]) ).
fof(f15858,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),element_relation)
| ~ member(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),universal_class)
| null_class = intersection(X0,complement(compose(element_relation,complement(singleton_relation))))
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
| ~ spl0_235
| ~ spl0_839 ),
inference(forward_demodulation,[],[f15857,f2312]) ).
fof(f15857,plain,
( ! [X0] :
( ~ member(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),universal_class)
| null_class = intersection(X0,complement(compose(element_relation,complement(singleton_relation))))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
| ~ spl0_235
| ~ spl0_839 ),
inference(forward_demodulation,[],[f15856,f2312]) ).
fof(f15856,plain,
( ! [X0] :
( null_class = intersection(X0,complement(compose(element_relation,complement(singleton_relation))))
| ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
| ~ spl0_235
| ~ spl0_839 ),
inference(forward_demodulation,[],[f15854,f2312]) ).
fof(f15854,plain,
( ! [X0] :
( null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
| ~ spl0_839 ),
inference(avatar_component_clause,[],[f15853]) ).
fof(f15876,plain,
( spl0_842
| ~ spl0_144
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1693,f1660,f1167,f15874]) ).
fof(f1693,plain,
( ! [X0] :
( null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
| ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),identity_relation) )
| ~ spl0_144
| ~ spl0_196 ),
inference(resolution,[],[f1661,f1168]) ).
fof(f15868,plain,
( spl0_841
| ~ spl0_143
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1690,f1660,f1163,f15866]) ).
fof(f1690,plain,
( ! [X0] :
( null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0)
| ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
| ~ spl0_143
| ~ spl0_196 ),
inference(resolution,[],[f1661,f1164]) ).
fof(f15863,plain,
( spl0_840
| ~ spl0_144
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f1673,f1656,f1167,f15861]) ).
fof(f1673,plain,
( ! [X0] :
( null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation) )
| ~ spl0_144
| ~ spl0_195 ),
inference(resolution,[],[f1657,f1168]) ).
fof(f15855,plain,
( spl0_839
| ~ spl0_143
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f1670,f1656,f1163,f15853]) ).
fof(f1670,plain,
( ! [X0] :
( null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
| ~ spl0_143
| ~ spl0_195 ),
inference(resolution,[],[f1657,f1164]) ).
fof(f15792,plain,
( spl0_631
| spl0_838
| ~ spl0_79
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1482,f1452,f628,f15790,f9581]) ).
fof(f15790,plain,
( spl0_838
<=> ! [X0,X3] :
( ~ function(X0)
| domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = unordered_pair(unordered_pair(first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))))),unordered_pair(first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),unordered_pair(second(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),second(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))))))
| ~ member(X3,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f1482,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,cross_product(X1,X2))
| ~ member(X3,universal_class)
| domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = unordered_pair(unordered_pair(first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))))),unordered_pair(first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),unordered_pair(second(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),second(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))))))) )
| ~ spl0_79
| ~ spl0_170 ),
inference(resolution,[],[f1453,f629]) ).
fof(f15776,plain,
( spl0_837
| ~ spl0_198
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1940,f1935,f1711,f15774]) ).
fof(f15774,plain,
( spl0_837
<=> ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)),X2))
| ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f1940,plain,
( ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)),X2))
| ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)
| cross_product(X0,X1) = null_class )
| ~ spl0_198
| ~ spl0_209 ),
inference(superposition,[],[f1936,f1712]) ).
fof(f15772,plain,
( spl0_836
| ~ spl0_39
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f3157,f2727,f376,f15770]) ).
fof(f2727,plain,
( spl0_284
<=> ! [X0] : subclass(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f3157,plain,
( ! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 )
| ~ spl0_39
| ~ spl0_284 ),
inference(resolution,[],[f2728,f377]) ).
fof(f2728,plain,
( ! [X0] : subclass(null_class,X0)
| ~ spl0_284 ),
inference(avatar_component_clause,[],[f2727]) ).
fof(f15768,plain,
( spl0_834
| ~ spl0_835
| ~ spl0_99
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f843,f802,f739,f15765,f15762]) ).
fof(f15762,plain,
( spl0_834
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f15765,plain,
( spl0_835
<=> subclass(universal_class,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f843,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) )
| ~ spl0_99
| ~ spl0_106 ),
inference(resolution,[],[f803,f740]) ).
fof(f15734,plain,
( spl0_833
| ~ spl0_176
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2009,f1994,f1477,f15732]) ).
fof(f15732,plain,
( spl0_833
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(element_relation))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f1477,plain,
( spl0_176
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f2009,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(element_relation))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class) )
| ~ spl0_176
| ~ spl0_211 ),
inference(resolution,[],[f1995,f1478]) ).
fof(f1478,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1477]) ).
fof(f15727,plain,
( ~ spl0_831
| ~ spl0_832
| spl0_633
| ~ spl0_162
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f1647,f1639,f1351,f9659,f15724,f15720]) ).
fof(f15720,plain,
( spl0_831
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f15724,plain,
( spl0_832
<=> member(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f9659,plain,
( spl0_633
<=> null_class = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f1647,plain,
( null_class = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
| ~ spl0_162
| ~ spl0_194 ),
inference(resolution,[],[f1640,f1352]) ).
fof(f15668,plain,
( spl0_830
| ~ spl0_176
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2049,f1998,f1477,f15666]) ).
fof(f15666,plain,
( spl0_830
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(element_relation))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f2049,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(element_relation))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
| ~ spl0_176
| ~ spl0_212 ),
inference(duplicate_literal_removal,[],[f2032]) ).
fof(f2032,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(element_relation))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
| ~ spl0_176
| ~ spl0_212 ),
inference(resolution,[],[f1999,f1478]) ).
fof(f15664,plain,
( spl0_829
| ~ spl0_89
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1938,f1935,f682,f15662]) ).
fof(f15662,plain,
( spl0_829
<=> ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class))),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f682,plain,
( spl0_89
<=> ! [X4,X7,X5,X1] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f1938,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class))),universal_class))))) )
| ~ spl0_89
| ~ spl0_209 ),
inference(resolution,[],[f1936,f683]) ).
fof(f683,plain,
( ! [X1,X7,X4,X5] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) )
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f682]) ).
fof(f15582,plain,
( spl0_828
| ~ spl0_235
| ~ spl0_822 ),
inference(avatar_split_clause,[],[f15551,f15548,f2310,f15580]) ).
fof(f15580,plain,
( spl0_828
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation)
| ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ operation(X2)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f15548,plain,
( spl0_822
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ operation(X2)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f15551,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation)
| ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ operation(X2)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) )
| ~ spl0_235
| ~ spl0_822 ),
inference(forward_demodulation,[],[f15549,f2312]) ).
fof(f15549,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ operation(X2)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),identity_relation) )
| ~ spl0_822 ),
inference(avatar_component_clause,[],[f15548]) ).
fof(f15578,plain,
( spl0_827
| ~ spl0_235
| ~ spl0_821 ),
inference(avatar_split_clause,[],[f15546,f15543,f2310,f15576]) ).
fof(f15576,plain,
( spl0_827
<=> ! [X2,X0,X1] :
( ~ subclass(domain_of(X1),complement(compose(element_relation,complement(singleton_relation))))
| ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ operation(X2)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f15543,plain,
( spl0_821
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),complement(compose(element_relation,complement(identity_relation))))
| ~ operation(X2)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f15546,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_of(X1),complement(compose(element_relation,complement(singleton_relation))))
| ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ operation(X2)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation) )
| ~ spl0_235
| ~ spl0_821 ),
inference(forward_demodulation,[],[f15544,f2312]) ).
fof(f15544,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),complement(compose(element_relation,complement(identity_relation))))
| ~ operation(X2)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation) )
| ~ spl0_821 ),
inference(avatar_component_clause,[],[f15543]) ).
fof(f15567,plain,
( spl0_826
| ~ spl0_198
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1932,f1923,f1711,f15565]) ).
fof(f15565,plain,
( spl0_826
<=> ! [X0,X3,X2,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| member(regular(cross_product(X0,X1)),compose(X2,X3))
| ~ member(second(regular(cross_product(X0,X1))),universal_class)
| null_class = intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f1932,plain,
( ! [X2,X3,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| member(regular(cross_product(X0,X1)),compose(X2,X3))
| ~ member(second(regular(cross_product(X0,X1))),universal_class)
| null_class = intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| cross_product(X0,X1) = null_class )
| ~ spl0_198
| ~ spl0_208 ),
inference(superposition,[],[f1924,f1712]) ).
fof(f15563,plain,
( spl0_825
| ~ spl0_152
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1853,f1812,f1247,f15561]) ).
fof(f15561,plain,
( spl0_825
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f1247,plain,
( spl0_152
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(universal_class,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1853,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class) )
| ~ spl0_152
| ~ spl0_204 ),
inference(resolution,[],[f1813,f1248]) ).
fof(f1248,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,universal_class) )
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f1247]) ).
fof(f15559,plain,
( spl0_824
| ~ spl0_152
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1827,f1803,f1247,f15557]) ).
fof(f15557,plain,
( spl0_824
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f1827,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X1,universal_class) )
| ~ spl0_152
| ~ spl0_202 ),
inference(resolution,[],[f1804,f1248]) ).
fof(f15555,plain,
( spl0_823
| ~ spl0_142
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1770,f1745,f1159,f15553]) ).
fof(f15553,plain,
( spl0_823
<=> ! [X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),regular(X3))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),null_class)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3)
| null_class = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f1770,plain,
( ! [X2,X3,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),regular(X3))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),null_class)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3)
| null_class = X3 )
| ~ spl0_142
| ~ spl0_199 ),
inference(resolution,[],[f1746,f1160]) ).
fof(f15550,plain,
( spl0_822
| ~ spl0_144
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1767,f1745,f1167,f15548]) ).
fof(f1767,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ operation(X2)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),identity_relation) )
| ~ spl0_144
| ~ spl0_199 ),
inference(resolution,[],[f1746,f1168]) ).
fof(f15545,plain,
( spl0_821
| ~ spl0_143
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1764,f1745,f1163,f15543]) ).
fof(f1764,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),complement(compose(element_relation,complement(identity_relation))))
| ~ operation(X2)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation) )
| ~ spl0_143
| ~ spl0_199 ),
inference(resolution,[],[f1746,f1164]) ).
fof(f15541,plain,
( spl0_820
| ~ spl0_93
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1267,f1247,f702,f15539]) ).
fof(f15539,plain,
( spl0_820
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X3,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f1267,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X3,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_152 ),
inference(resolution,[],[f1248,f703]) ).
fof(f15512,plain,
( spl0_819
| ~ spl0_786
| ~ spl0_817 ),
inference(avatar_split_clause,[],[f15503,f15500,f14703,f15510]) ).
fof(f15510,plain,
( spl0_819
<=> ! [X2,X0,X1] :
( ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(null_class,X2),universal_class)))))
| member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f15500,plain,
( spl0_817
<=> ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
| ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f15503,plain,
( ! [X2,X0,X1] :
( ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(null_class,X2),universal_class)))))
| member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| cross_product(X0,X1) = null_class )
| ~ spl0_786
| ~ spl0_817 ),
inference(forward_demodulation,[],[f15501,f14705]) ).
fof(f15501,plain,
( ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
| ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| cross_product(X0,X1) = null_class )
| ~ spl0_817 ),
inference(avatar_component_clause,[],[f15500]) ).
fof(f15508,plain,
( ~ spl0_818
| ~ spl0_22
| spl0_813 ),
inference(avatar_split_clause,[],[f15283,f15279,f295,f15505]) ).
fof(f15505,plain,
( spl0_818
<=> function(composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f15283,plain,
( ~ function(composition_function)
| ~ spl0_22
| spl0_813 ),
inference(resolution,[],[f15281,f296]) ).
fof(f15502,plain,
( spl0_817
| ~ spl0_198
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f1911,f1906,f1711,f15500]) ).
fof(f1911,plain,
( ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
| ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| cross_product(X0,X1) = null_class )
| ~ spl0_198
| ~ spl0_206 ),
inference(superposition,[],[f1907,f1712]) ).
fof(f15498,plain,
( spl0_816
| ~ spl0_48
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1758,f1745,f444,f15496]) ).
fof(f15496,plain,
( spl0_816
<=> ! [X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),unordered_pair(X3,X4))
| ~ operation(X2)
| unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))) = X3
| unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f1758,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),unordered_pair(X3,X4))
| ~ operation(X2)
| unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))) = X3
| unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))) = X4 )
| ~ spl0_48
| ~ spl0_199 ),
inference(resolution,[],[f1746,f445]) ).
fof(f15291,plain,
( spl0_815
| ~ spl0_77
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2030,f1998,f613,f15289]) ).
fof(f15289,plain,
( spl0_815
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(X3,X4)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X2,X4)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f2030,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(X3,X4)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X2,X4)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) )
| ~ spl0_77
| ~ spl0_212 ),
inference(resolution,[],[f1999,f614]) ).
fof(f15287,plain,
( spl0_814
| ~ spl0_77
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2007,f1994,f613,f15285]) ).
fof(f15285,plain,
( spl0_814
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(X3,X4)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X0,X4)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f2007,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(X3,X4)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X0,X4)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3) )
| ~ spl0_77
| ~ spl0_211 ),
inference(resolution,[],[f1995,f614]) ).
fof(f15282,plain,
( spl0_812
| ~ spl0_813
| ~ spl0_85
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1877,f1868,f664,f15279,f15276]) ).
fof(f15276,plain,
( spl0_812
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f664,plain,
( spl0_85
<=> ! [X0,X1] :
( ~ member(X0,X1)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1877,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation)
| ~ member(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))) )
| ~ spl0_85
| ~ spl0_205 ),
inference(resolution,[],[f1869,f665]) ).
fof(f665,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1) )
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f15274,plain,
( spl0_811
| ~ spl0_48
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1684,f1660,f444,f15272]) ).
fof(f15272,plain,
( spl0_811
<=> ! [X2,X0,X1] :
( null_class = intersection(unordered_pair(X0,X1),X2)
| ~ member(intersection(unordered_pair(X0,X1),X2),universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f1684,plain,
( ! [X2,X0,X1] :
( null_class = intersection(unordered_pair(X0,X1),X2)
| ~ member(intersection(unordered_pair(X0,X1),X2),universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X1 )
| ~ spl0_48
| ~ spl0_196 ),
inference(resolution,[],[f1661,f445]) ).
fof(f15270,plain,
( spl0_810
| ~ spl0_48
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f1664,f1656,f444,f15268]) ).
fof(f15268,plain,
( spl0_810
<=> ! [X2,X0,X1] :
( null_class = intersection(X0,unordered_pair(X1,X2))
| ~ member(intersection(X0,unordered_pair(X1,X2)),universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f1664,plain,
( ! [X2,X0,X1] :
( null_class = intersection(X0,unordered_pair(X1,X2))
| ~ member(intersection(X0,unordered_pair(X1,X2)),universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X2 )
| ~ spl0_48
| ~ spl0_195 ),
inference(resolution,[],[f1657,f445]) ).
fof(f15266,plain,
( spl0_809
| ~ spl0_96
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1419,f1369,f727,f15264]) ).
fof(f15264,plain,
( spl0_809
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,flip(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f1419,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,flip(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),X0) )
| ~ spl0_96
| ~ spl0_165 ),
inference(resolution,[],[f1370,f728]) ).
fof(f15260,plain,
( ~ spl0_808
| ~ spl0_235
| spl0_806 ),
inference(avatar_split_clause,[],[f15252,f15244,f2310,f15257]) ).
fof(f15257,plain,
( spl0_808
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f15244,plain,
( spl0_806
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f15252,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),singleton_relation)
| ~ spl0_235
| spl0_806 ),
inference(forward_demodulation,[],[f15245,f2312]) ).
fof(f15245,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),identity_relation)
| spl0_806 ),
inference(avatar_component_clause,[],[f15244]) ).
fof(f15251,plain,
( spl0_527
| ~ spl0_805
| spl0_806
| ~ spl0_807
| ~ spl0_84
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1209,f1167,f654,f15248,f15244,f15240,f7413]) ).
fof(f7413,plain,
( spl0_527
<=> null_class = domain_of(flip(cross_product(subset_relation,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f15248,plain,
( spl0_807
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f1209,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),identity_relation)
| ~ member(domain_of(flip(cross_product(subset_relation,universal_class))),universal_class)
| null_class = domain_of(flip(cross_product(subset_relation,universal_class)))
| ~ spl0_84
| ~ spl0_144 ),
inference(resolution,[],[f1168,f655]) ).
fof(f15236,plain,
( ~ spl0_804
| ~ spl0_235
| spl0_788 ),
inference(avatar_split_clause,[],[f14809,f14800,f2310,f15233]) ).
fof(f15233,plain,
( spl0_804
<=> subset_relation = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f14800,plain,
( spl0_788
<=> identity_relation = subset_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f14809,plain,
( subset_relation != singleton_relation
| ~ spl0_235
| spl0_788 ),
inference(forward_demodulation,[],[f14801,f2312]) ).
fof(f14801,plain,
( identity_relation != subset_relation
| spl0_788 ),
inference(avatar_component_clause,[],[f14800]) ).
fof(f15228,plain,
( ~ spl0_803
| ~ spl0_235
| spl0_799 ),
inference(avatar_split_clause,[],[f15212,f15203,f2310,f15225]) ).
fof(f15225,plain,
( spl0_803
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(singleton_relation))),complement(compose(element_relation,complement(singleton_relation)))),universal_class)),universal_class))))))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f15203,plain,
( spl0_799
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f15212,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(singleton_relation))),complement(compose(element_relation,complement(singleton_relation)))),universal_class)),universal_class))))))),singleton_relation)
| ~ spl0_235
| spl0_799 ),
inference(forward_demodulation,[],[f15204,f2312]) ).
fof(f15204,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),singleton_relation)
| spl0_799 ),
inference(avatar_component_clause,[],[f15203]) ).
fof(f15223,plain,
( ~ spl0_802
| ~ spl0_235
| spl0_800 ),
inference(avatar_split_clause,[],[f15211,f15207,f2310,f15220]) ).
fof(f15220,plain,
( spl0_802
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(singleton_relation))),complement(compose(element_relation,complement(singleton_relation)))),universal_class)),universal_class))))))),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f15207,plain,
( spl0_800
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f15211,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(singleton_relation))),complement(compose(element_relation,complement(singleton_relation)))),universal_class)),universal_class))))))),element_relation)
| ~ spl0_235
| spl0_800 ),
inference(forward_demodulation,[],[f15209,f2312]) ).
fof(f15209,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),element_relation)
| spl0_800 ),
inference(avatar_component_clause,[],[f15207]) ).
fof(f15218,plain,
( ~ spl0_801
| ~ spl0_235
| spl0_798 ),
inference(avatar_split_clause,[],[f15213,f15199,f2310,f15215]) ).
fof(f15215,plain,
( spl0_801
<=> member(complement(compose(element_relation,complement(singleton_relation))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f15199,plain,
( spl0_798
<=> member(complement(compose(element_relation,complement(identity_relation))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f15213,plain,
( ~ member(complement(compose(element_relation,complement(singleton_relation))),universal_class)
| ~ spl0_235
| spl0_798 ),
inference(forward_demodulation,[],[f15201,f2312]) ).
fof(f15201,plain,
( ~ member(complement(compose(element_relation,complement(identity_relation))),universal_class)
| spl0_798 ),
inference(avatar_component_clause,[],[f15199]) ).
fof(f15210,plain,
( spl0_521
| ~ spl0_798
| spl0_799
| ~ spl0_800
| ~ spl0_84
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1195,f1163,f654,f15207,f15203,f15199,f7371]) ).
fof(f7371,plain,
( spl0_521
<=> null_class = complement(compose(element_relation,complement(identity_relation))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f1195,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),singleton_relation)
| ~ member(complement(compose(element_relation,complement(identity_relation))),universal_class)
| null_class = complement(compose(element_relation,complement(identity_relation)))
| ~ spl0_84
| ~ spl0_143 ),
inference(resolution,[],[f1164,f655]) ).
fof(f15187,plain,
( spl0_797
| ~ spl0_38
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1939,f1935,f372,f15185]) ).
fof(f15185,plain,
( spl0_797
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
| ~ subclass(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),X2),X3)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f1939,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
| ~ subclass(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),X2),X3)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) )
| ~ spl0_38
| ~ spl0_209 ),
inference(resolution,[],[f1936,f373]) ).
fof(f15003,plain,
( ~ spl0_796
| ~ spl0_235
| spl0_789 ),
inference(avatar_split_clause,[],[f14808,f14804,f2310,f15000]) ).
fof(f15000,plain,
( spl0_796
<=> subclass(subset_relation,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f14804,plain,
( spl0_789
<=> subclass(subset_relation,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f14808,plain,
( ~ subclass(subset_relation,singleton_relation)
| ~ spl0_235
| spl0_789 ),
inference(forward_demodulation,[],[f14806,f2312]) ).
fof(f14806,plain,
( ~ subclass(subset_relation,identity_relation)
| spl0_789 ),
inference(avatar_component_clause,[],[f14804]) ).
fof(f14998,plain,
( spl0_795
| ~ spl0_154
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f1785,f1773,f1277,f14996]) ).
fof(f14996,plain,
( spl0_795
<=> ! [X0] :
( not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)))),unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),unordered_pair(second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))))))
| cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f1277,plain,
( spl0_154
<=> ! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
| cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1773,plain,
( spl0_200
<=> ! [X2,X0,X1] :
( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
| subclass(cross_product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f1785,plain,
( ! [X0] :
( not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)))),unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),unordered_pair(second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))))))
| cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
| ~ spl0_154
| ~ spl0_200 ),
inference(resolution,[],[f1774,f1278]) ).
fof(f1278,plain,
( ! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
| cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f1277]) ).
fof(f1774,plain,
( ! [X2,X0,X1] :
( subclass(cross_product(X0,X1),X2)
| not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2))))) )
| ~ spl0_200 ),
inference(avatar_component_clause,[],[f1773]) ).
fof(f14994,plain,
( spl0_794
| ~ spl0_153
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f1784,f1773,f1273,f14992]) ).
fof(f14992,plain,
( spl0_794
<=> ! [X0] :
( not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)))),unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),unordered_pair(second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))))))
| rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f1273,plain,
( spl0_153
<=> ! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
| rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1784,plain,
( ! [X0] :
( not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)))),unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),unordered_pair(second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))))))
| rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) )
| ~ spl0_153
| ~ spl0_200 ),
inference(resolution,[],[f1774,f1274]) ).
fof(f1274,plain,
( ! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
| rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) )
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f1273]) ).
fof(f14855,plain,
( spl0_793
| ~ spl0_786
| ~ spl0_792 ),
inference(avatar_split_clause,[],[f14851,f14848,f14703,f14853]) ).
fof(f14853,plain,
( spl0_793
<=> ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(X2,X2),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f14848,plain,
( spl0_792
<=> ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(X2,X2),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f14851,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(X2,X2),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
| ~ spl0_786
| ~ spl0_792 ),
inference(forward_demodulation,[],[f14849,f14705]) ).
fof(f14849,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(X2,X2),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
| ~ spl0_792 ),
inference(avatar_component_clause,[],[f14848]) ).
fof(f14850,plain,
( spl0_792
| ~ spl0_89
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f1909,f1906,f682,f14848]) ).
fof(f1909,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(X2,X2),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
| ~ spl0_89
| ~ spl0_206 ),
inference(resolution,[],[f1907,f683]) ).
fof(f14846,plain,
( spl0_791
| ~ spl0_142
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1695,f1660,f1159,f14844]) ).
fof(f14844,plain,
( spl0_791
<=> ! [X0,X1] :
( null_class = intersection(regular(X0),X1)
| ~ member(intersection(regular(X0),X1),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),null_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f1695,plain,
( ! [X0,X1] :
( null_class = intersection(regular(X0),X1)
| ~ member(intersection(regular(X0),X1),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),null_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),X0)
| null_class = X0 )
| ~ spl0_142
| ~ spl0_196 ),
inference(resolution,[],[f1661,f1160]) ).
fof(f14842,plain,
( spl0_790
| ~ spl0_142
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f1675,f1656,f1159,f14840]) ).
fof(f14840,plain,
( spl0_790
<=> ! [X0,X1] :
( null_class = intersection(X0,regular(X1))
| ~ member(intersection(X0,regular(X1)),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),null_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),X1)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f1675,plain,
( ! [X0,X1] :
( null_class = intersection(X0,regular(X1))
| ~ member(intersection(X0,regular(X1)),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),null_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),X1)
| null_class = X1 )
| ~ spl0_142
| ~ spl0_195 ),
inference(resolution,[],[f1657,f1160]) ).
fof(f14807,plain,
( spl0_788
| ~ spl0_789
| ~ spl0_39
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2693,f2466,f376,f14804,f14800]) ).
fof(f2466,plain,
( spl0_264
<=> subclass(identity_relation,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f2693,plain,
( ~ subclass(subset_relation,identity_relation)
| identity_relation = subset_relation
| ~ spl0_39
| ~ spl0_264 ),
inference(resolution,[],[f2468,f377]) ).
fof(f2468,plain,
( subclass(identity_relation,subset_relation)
| ~ spl0_264 ),
inference(avatar_component_clause,[],[f2466]) ).
fof(f14709,plain,
( spl0_786
| spl0_787
| ~ spl0_40
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1942,f1935,f380,f14707,f14703]) ).
fof(f14707,plain,
( spl0_787
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,domain_of(domain_of(flip(cross_product(null_class,universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f1942,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(X1,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_40
| ~ spl0_209 ),
inference(superposition,[],[f1936,f381]) ).
fof(f14701,plain,
( spl0_785
| ~ spl0_40
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1839,f1803,f380,f14699]) ).
fof(f14699,plain,
( spl0_785
<=> ! [X2,X0,X1] :
( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f1839,plain,
( ! [X2,X0,X1] :
( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class) )
| ~ spl0_40
| ~ spl0_202 ),
inference(superposition,[],[f1804,f381]) ).
fof(f14694,plain,
( spl0_783
| ~ spl0_784
| ~ spl0_40
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f1800,f1793,f380,f14691,f14688]) ).
fof(f14688,plain,
( spl0_783
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f14691,plain,
( spl0_784
<=> inductive(domain_of(domain_of(flip(cross_product(null_class,universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f1793,plain,
( spl0_201
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
| ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f1800,plain,
( ! [X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
| ~ spl0_40
| ~ spl0_201 ),
inference(superposition,[],[f1794,f381]) ).
fof(f1794,plain,
( ! [X2,X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2)) )
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f1793]) ).
fof(f14686,plain,
( spl0_782
| ~ spl0_158
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1508,f1456,f1294,f14684]) ).
fof(f14684,plain,
( spl0_782
<=> ! [X0] :
( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class))))
| ~ member(X0,universal_class)
| null_class = cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f1508,plain,
( ! [X0] :
( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class))))
| ~ member(X0,universal_class)
| null_class = cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class) )
| ~ spl0_158
| ~ spl0_171 ),
inference(resolution,[],[f1457,f1295]) ).
fof(f14633,plain,
( spl0_781
| ~ spl0_49
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f1646,f1639,f448,f14631]) ).
fof(f14631,plain,
( spl0_781
<=> ! [X0,X1] :
( complement(intersection(X0,X1)) = null_class
| ~ member(complement(intersection(X0,X1)),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X1)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f1646,plain,
( ! [X0,X1] :
( complement(intersection(X0,X1)) = null_class
| ~ member(complement(intersection(X0,X1)),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X1)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X0) )
| ~ spl0_49
| ~ spl0_194 ),
inference(resolution,[],[f1640,f449]) ).
fof(f14603,plain,
( spl0_780
| ~ spl0_185
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1628,f1620,f1556,f14601]) ).
fof(f14601,plain,
( spl0_780
<=> ! [X0] :
( null_class = X0
| ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f1628,plain,
( ! [X0] :
( null_class = X0
| ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_185
| ~ spl0_193 ),
inference(resolution,[],[f1621,f1557]) ).
fof(f14519,plain,
( spl0_779
| ~ spl0_130
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1859,f1812,f1012,f14517]) ).
fof(f14517,plain,
( spl0_779
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
| subclass(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f1859,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
| subclass(X1,X2) )
| ~ spl0_130
| ~ spl0_204 ),
inference(resolution,[],[f1813,f1013]) ).
fof(f14515,plain,
( spl0_778
| ~ spl0_130
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1833,f1803,f1012,f14513]) ).
fof(f14513,plain,
( spl0_778
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
| subclass(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f1833,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
| subclass(X1,X2) )
| ~ spl0_130
| ~ spl0_202 ),
inference(resolution,[],[f1804,f1013]) ).
fof(f14511,plain,
( spl0_777
| ~ spl0_114
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f1789,f1773,f892,f14509]) ).
fof(f14509,plain,
( spl0_777
<=> ! [X0,X1] :
( not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class)))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),unordered_pair(second(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),second(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))))))
| function(cross_product(X0,X1))
| ~ single_valued_class(cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f892,plain,
( spl0_114
<=> ! [X0] :
( ~ subclass(X0,cross_product(universal_class,universal_class))
| function(X0)
| ~ single_valued_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1789,plain,
( ! [X0,X1] :
( not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class)))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),unordered_pair(second(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),second(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))))))
| function(cross_product(X0,X1))
| ~ single_valued_class(cross_product(X0,X1)) )
| ~ spl0_114
| ~ spl0_200 ),
inference(resolution,[],[f1774,f893]) ).
fof(f893,plain,
( ! [X0] :
( ~ subclass(X0,cross_product(universal_class,universal_class))
| function(X0)
| ~ single_valued_class(X0) )
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f892]) ).
fof(f14507,plain,
( spl0_776
| ~ spl0_93
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1068,f1012,f702,f14505]) ).
fof(f14505,plain,
( spl0_776
<=> ! [X4,X0,X3,X2,X1] :
( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| subclass(X0,X4)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f1068,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| subclass(X0,X4)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_130 ),
inference(resolution,[],[f1013,f703]) ).
fof(f14335,plain,
( spl0_775
| ~ spl0_146
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f1779,f1773,f1221,f14333]) ).
fof(f14333,plain,
( spl0_775
<=> ! [X0,X1] :
( not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1)))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),second(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))))))
| cross_product(universal_class,universal_class) = compose(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f1221,plain,
( spl0_146
<=> ! [X0,X1] :
( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
| cross_product(universal_class,universal_class) = compose(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1779,plain,
( ! [X0,X1] :
( not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1)))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),second(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))))))
| cross_product(universal_class,universal_class) = compose(X0,X1) )
| ~ spl0_146
| ~ spl0_200 ),
inference(resolution,[],[f1774,f1222]) ).
fof(f1222,plain,
( ! [X0,X1] :
( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
| cross_product(universal_class,universal_class) = compose(X0,X1) )
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f1221]) ).
fof(f14331,plain,
( spl0_774
| ~ spl0_158
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1432,f1369,f1294,f14329]) ).
fof(f14329,plain,
( spl0_774
<=> ! [X0] :
( ~ subclass(domain_relation,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class))))
| ~ member(X0,universal_class)
| null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f1432,plain,
( ! [X0] :
( ~ subclass(domain_relation,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class))))
| ~ member(X0,universal_class)
| null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class) )
| ~ spl0_158
| ~ spl0_165 ),
inference(resolution,[],[f1370,f1295]) ).
fof(f14327,plain,
( spl0_773
| ~ spl0_79
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1132,f1087,f628,f14325]) ).
fof(f14325,plain,
( spl0_773
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,cross_product(X1,X2)),X3)
| not_subclass_element(intersection(X0,cross_product(X1,X2)),X3) = unordered_pair(unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))),unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),unordered_pair(second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f1132,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,cross_product(X1,X2)),X3)
| not_subclass_element(intersection(X0,cross_product(X1,X2)),X3) = unordered_pair(unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))),unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),unordered_pair(second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))))) )
| ~ spl0_79
| ~ spl0_135 ),
inference(resolution,[],[f1088,f629]) ).
fof(f14323,plain,
( spl0_772
| ~ spl0_79
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1114,f1083,f628,f14321]) ).
fof(f14321,plain,
( spl0_772
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(cross_product(X0,X1),X2),X3)
| not_subclass_element(intersection(cross_product(X0,X1),X2),X3) = unordered_pair(unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))),unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),unordered_pair(second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f1114,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(cross_product(X0,X1),X2),X3)
| not_subclass_element(intersection(cross_product(X0,X1),X2),X3) = unordered_pair(unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))),unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),unordered_pair(second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))))) )
| ~ spl0_79
| ~ spl0_134 ),
inference(resolution,[],[f1084,f629]) ).
fof(f14265,plain,
( spl0_771
| ~ spl0_38
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f1910,f1906,f372,f14263]) ).
fof(f14263,plain,
( spl0_771
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(X2,X2),universal_class)
| ~ subclass(compose(X1,regular(cross_product(unordered_pair(X2,X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f1910,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(X2,X2),universal_class)
| ~ subclass(compose(X1,regular(cross_product(unordered_pair(X2,X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X3) )
| ~ spl0_38
| ~ spl0_206 ),
inference(resolution,[],[f1907,f373]) ).
fof(f14250,plain,
( spl0_769
| ~ spl0_770
| ~ spl0_39
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2533,f2393,f376,f14247,f14243]) ).
fof(f14243,plain,
( spl0_769
<=> element_relation = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f14247,plain,
( spl0_770
<=> subclass(element_relation,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f2393,plain,
( spl0_251
<=> subclass(singleton_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f2533,plain,
( ~ subclass(element_relation,singleton_relation)
| element_relation = singleton_relation
| ~ spl0_39
| ~ spl0_251 ),
inference(resolution,[],[f2395,f377]) ).
fof(f2395,plain,
( subclass(singleton_relation,element_relation)
| ~ spl0_251 ),
inference(avatar_component_clause,[],[f2393]) ).
fof(f14027,plain,
( spl0_768
| ~ spl0_106
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1858,f1812,f802,f14025]) ).
fof(f14025,plain,
( spl0_768
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f1858,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class))))) )
| ~ spl0_106
| ~ spl0_204 ),
inference(resolution,[],[f1813,f803]) ).
fof(f14023,plain,
( spl0_767
| ~ spl0_70
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1841,f1812,f568,f14021]) ).
fof(f14021,plain,
( spl0_767
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class)
| null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f1841,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class)
| null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) )
| ~ spl0_70
| ~ spl0_204 ),
inference(resolution,[],[f1813,f569]) ).
fof(f14019,plain,
( spl0_766
| ~ spl0_106
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1832,f1803,f802,f14017]) ).
fof(f14017,plain,
( spl0_766
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f1832,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) )
| ~ spl0_106
| ~ spl0_202 ),
inference(resolution,[],[f1804,f803]) ).
fof(f14015,plain,
( spl0_765
| ~ spl0_70
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1815,f1803,f568,f14013]) ).
fof(f14013,plain,
( spl0_765
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class)
| null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f1815,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class)
| null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_70
| ~ spl0_202 ),
inference(resolution,[],[f1804,f569]) ).
fof(f13964,plain,
( spl0_764
| ~ spl0_184
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f1786,f1773,f1549,f13962]) ).
fof(f13962,plain,
( spl0_764
<=> ! [X4,X0,X3,X2,X1] :
( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
| ~ member(X3,X0)
| ~ member(X4,X1)
| member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f1549,plain,
( spl0_184
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| ~ subclass(cross_product(X3,X1),X4)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1786,plain,
( ! [X2,X3,X0,X1,X4] :
( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
| ~ member(X3,X0)
| ~ member(X4,X1)
| member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),X2) )
| ~ spl0_184
| ~ spl0_200 ),
inference(resolution,[],[f1774,f1550]) ).
fof(f1550,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(cross_product(X3,X1),X4)
| ~ member(X2,X3)
| ~ member(X0,X1)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) )
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1549]) ).
fof(f13960,plain,
( spl0_763
| ~ spl0_158
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1490,f1452,f1294,f13958]) ).
fof(f13958,plain,
( spl0_763
<=> ! [X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class))))
| ~ member(X1,universal_class)
| null_class = cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f1490,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class))))
| ~ member(X1,universal_class)
| null_class = cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class) )
| ~ spl0_158
| ~ spl0_170 ),
inference(resolution,[],[f1453,f1295]) ).
fof(f13956,plain,
( spl0_762
| ~ spl0_93
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f851,f802,f702,f13954]) ).
fof(f13954,plain,
( spl0_762
<=> ! [X4,X0,X3,X2,X1] :
( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f851,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_106 ),
inference(resolution,[],[f803,f703]) ).
fof(f13862,plain,
( spl0_761
| ~ spl0_116
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1856,f1812,f919,f13860]) ).
fof(f13860,plain,
( spl0_761
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f1856,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| null_class = X1 )
| ~ spl0_116
| ~ spl0_204 ),
inference(resolution,[],[f1813,f920]) ).
fof(f13858,plain,
( spl0_760
| ~ spl0_116
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1830,f1803,f919,f13856]) ).
fof(f13856,plain,
( spl0_760
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f1830,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| null_class = X1 )
| ~ spl0_116
| ~ spl0_202 ),
inference(resolution,[],[f1804,f920]) ).
fof(f13782,plain,
( spl0_759
| ~ spl0_44
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f1648,f1639,f424,f13780]) ).
fof(f13780,plain,
( spl0_759
<=> ! [X0] :
( null_class = complement(complement(X0))
| ~ member(complement(complement(X0)),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),X0)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f1648,plain,
( ! [X0] :
( null_class = complement(complement(X0))
| ~ member(complement(complement(X0)),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),X0)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),universal_class) )
| ~ spl0_44
| ~ spl0_194 ),
inference(resolution,[],[f1640,f425]) ).
fof(f13778,plain,
( spl0_758
| ~ spl0_163
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1617,f1609,f1361,f13776]) ).
fof(f13776,plain,
( spl0_758
<=> ! [X0,X1] :
( ~ inductive(unordered_pair(X0,X1))
| unordered_pair(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))
| not_subclass_element(unordered_pair(X0,X1),domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))) = X1
| not_subclass_element(unordered_pair(X0,X1),domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f1361,plain,
( spl0_163
<=> ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X0
| not_subclass_element(unordered_pair(X0,X1),X2) = X1
| subclass(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1609,plain,
( spl0_191
<=> ! [X0] :
( ~ inductive(X0)
| ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
| domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1617,plain,
( ! [X0,X1] :
( ~ inductive(unordered_pair(X0,X1))
| unordered_pair(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))
| not_subclass_element(unordered_pair(X0,X1),domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))) = X1
| not_subclass_element(unordered_pair(X0,X1),domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))) = X0 )
| ~ spl0_163
| ~ spl0_191 ),
inference(resolution,[],[f1610,f1362]) ).
fof(f1362,plain,
( ! [X2,X0,X1] :
( subclass(unordered_pair(X0,X1),X2)
| not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0 )
| ~ spl0_163 ),
inference(avatar_component_clause,[],[f1361]) ).
fof(f1610,plain,
( ! [X0] :
( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
| ~ inductive(X0)
| domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 )
| ~ spl0_191 ),
inference(avatar_component_clause,[],[f1609]) ).
fof(f13774,plain,
( spl0_757
| ~ spl0_93
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f979,f919,f702,f13772]) ).
fof(f13772,plain,
( spl0_757
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| null_class = X0
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f979,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| null_class = X0
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_116 ),
inference(resolution,[],[f920,f703]) ).
fof(f13642,plain,
( spl0_756
| ~ spl0_106
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2026,f1998,f802,f13640]) ).
fof(f13640,plain,
( spl0_756
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f2026,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,X3) )
| ~ spl0_106
| ~ spl0_212 ),
inference(resolution,[],[f1999,f803]) ).
fof(f13638,plain,
( spl0_755
| ~ spl0_106
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2003,f1994,f802,f13636]) ).
fof(f13636,plain,
( spl0_755
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f2003,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,X3) )
| ~ spl0_106
| ~ spl0_211 ),
inference(resolution,[],[f1995,f803]) ).
fof(f13571,plain,
( spl0_754
| ~ spl0_111
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1927,f1923,f823,f13569]) ).
fof(f13569,plain,
( spl0_754
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X1,universal_class)
| null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f1927,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X1,universal_class)
| null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation) )
| ~ spl0_111
| ~ spl0_208 ),
inference(resolution,[],[f1924,f824]) ).
fof(f13567,plain,
( spl0_753
| ~ spl0_40
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1863,f1812,f380,f13565]) ).
fof(f13565,plain,
( spl0_753
<=> ! [X2,X0,X1] :
( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f1863,plain,
( ! [X2,X0,X1] :
( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_40
| ~ spl0_204 ),
inference(superposition,[],[f1813,f381]) ).
fof(f13563,plain,
( spl0_752
| ~ spl0_162
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1392,f1365,f1351,f13561]) ).
fof(f13561,plain,
( spl0_752
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1)
| subclass(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
| ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f1365,plain,
( spl0_164
<=> ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
| ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1392,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1)
| subclass(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
| ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) )
| ~ spl0_162
| ~ spl0_164 ),
inference(resolution,[],[f1366,f1352]) ).
fof(f1366,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
| ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2)) )
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f1365]) ).
fof(f13532,plain,
( spl0_751
| ~ spl0_38
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1888,f1868,f372,f13530]) ).
fof(f13530,plain,
( spl0_751
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,X0)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ subclass(X0,X3)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f1888,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,X0)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ subclass(X0,X3)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X3) )
| ~ spl0_38
| ~ spl0_205 ),
inference(resolution,[],[f1869,f373]) ).
fof(f13528,plain,
( spl0_750
| ~ spl0_40
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f1797,f1793,f380,f13526]) ).
fof(f13526,plain,
( spl0_750
<=> ! [X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f1797,plain,
( ! [X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_40
| ~ spl0_201 ),
inference(superposition,[],[f1794,f381]) ).
fof(f13466,plain,
( spl0_749
| spl0_631
| ~ spl0_79
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1261,f1247,f628,f9581,f13464]) ).
fof(f13464,plain,
( spl0_749
<=> ! [X2] :
( ~ member(X2,universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,X2))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),first(domain_of(intersection(element_relation,cross_product(universal_class,X2))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),second(domain_of(intersection(element_relation,cross_product(universal_class,X2))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f1261,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| ~ member(X2,universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,X2))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),first(domain_of(intersection(element_relation,cross_product(universal_class,X2))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),second(domain_of(intersection(element_relation,cross_product(universal_class,X2))))))) )
| ~ spl0_79
| ~ spl0_152 ),
inference(resolution,[],[f1248,f629]) ).
fof(f13442,plain,
( spl0_748
| ~ spl0_341
| ~ spl0_616 ),
inference(avatar_split_clause,[],[f13017,f9349,f3477,f13439]) ).
fof(f13439,plain,
( spl0_748
<=> null_class = intersection(universal_class,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f9349,plain,
( spl0_616
<=> ! [X0] : null_class = intersection(X0,complement(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f13017,plain,
( null_class = intersection(universal_class,null_class)
| ~ spl0_341
| ~ spl0_616 ),
inference(superposition,[],[f9350,f3479]) ).
fof(f9350,plain,
( ! [X0] : null_class = intersection(X0,complement(X0))
| ~ spl0_616 ),
inference(avatar_component_clause,[],[f9349]) ).
fof(f13146,plain,
( spl0_747
| ~ spl0_31
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1892,f1868,f335,f13144]) ).
fof(f13144,plain,
( spl0_747
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,intersection(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f335,plain,
( spl0_31
<=> ! [X4,X0,X1] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f1892,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,intersection(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))),X0) )
| ~ spl0_31
| ~ spl0_205 ),
inference(resolution,[],[f1869,f336]) ).
fof(f336,plain,
( ! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X0) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f13142,plain,
( spl0_746
| ~ spl0_32
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1891,f1868,f339,f13140]) ).
fof(f13140,plain,
( spl0_746
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,intersection(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f1891,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,intersection(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))),X1) )
| ~ spl0_32
| ~ spl0_205 ),
inference(resolution,[],[f1869,f340]) ).
fof(f13016,plain,
( spl0_745
| ~ spl0_89
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1881,f1868,f682,f13014]) ).
fof(f13014,plain,
( spl0_745
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,compose(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f1881,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,compose(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) )
| ~ spl0_89
| ~ spl0_205 ),
inference(resolution,[],[f1869,f683]) ).
fof(f13012,plain,
( spl0_744
| ~ spl0_85
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1750,f1745,f664,f13010]) ).
fof(f13010,plain,
( spl0_744
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
| ~ member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f1750,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
| ~ member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) )
| ~ spl0_85
| ~ spl0_199 ),
inference(resolution,[],[f1746,f665]) ).
fof(f13008,plain,
( spl0_743
| ~ spl0_163
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1743,f1711,f1361,f13006]) ).
fof(f13006,plain,
( spl0_743
<=> ! [X2,X0,X1] :
( subclass(regular(cross_product(X0,X1)),X2)
| unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
| unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f1743,plain,
( ! [X2,X0,X1] :
( subclass(regular(cross_product(X0,X1)),X2)
| unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
| unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
| cross_product(X0,X1) = null_class )
| ~ spl0_163
| ~ spl0_198 ),
inference(superposition,[],[f1362,f1712]) ).
fof(f13004,plain,
( spl0_742
| ~ spl0_91
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1725,f1711,f691,f13002]) ).
fof(f13002,plain,
( spl0_742
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
| second(regular(cross_product(X0,X1))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f691,plain,
( spl0_91
<=> ! [X4,X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))) = X4
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1725,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
| second(regular(cross_product(X0,X1))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))
| cross_product(X0,X1) = null_class )
| ~ spl0_91
| ~ spl0_198 ),
inference(superposition,[],[f692,f1712]) ).
fof(f692,plain,
( ! [X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))) = X4 )
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f691]) ).
fof(f13000,plain,
( spl0_741
| ~ spl0_84
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1181,f1159,f654,f12998]) ).
fof(f12998,plain,
( spl0_741
<=> ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),null_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),X0)
| null_class = X0
| ~ member(regular(X0),universal_class)
| null_class = regular(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f1181,plain,
( ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),null_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),X0)
| null_class = X0
| ~ member(regular(X0),universal_class)
| null_class = regular(X0) )
| ~ spl0_84
| ~ spl0_142 ),
inference(resolution,[],[f1160,f655]) ).
fof(f12996,plain,
( spl0_740
| ~ spl0_79
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1045,f1008,f628,f12994]) ).
fof(f12994,plain,
( spl0_740
<=> ! [X2,X0,X1] :
( null_class = intersection(X0,cross_product(X1,X2))
| regular(intersection(X0,cross_product(X1,X2))) = unordered_pair(unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),first(regular(intersection(X0,cross_product(X1,X2))))),unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),unordered_pair(second(regular(intersection(X0,cross_product(X1,X2)))),second(regular(intersection(X0,cross_product(X1,X2))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f1045,plain,
( ! [X2,X0,X1] :
( null_class = intersection(X0,cross_product(X1,X2))
| regular(intersection(X0,cross_product(X1,X2))) = unordered_pair(unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),first(regular(intersection(X0,cross_product(X1,X2))))),unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),unordered_pair(second(regular(intersection(X0,cross_product(X1,X2)))),second(regular(intersection(X0,cross_product(X1,X2))))))) )
| ~ spl0_79
| ~ spl0_129 ),
inference(resolution,[],[f1009,f629]) ).
fof(f12992,plain,
( spl0_739
| ~ spl0_79
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1029,f1004,f628,f12990]) ).
fof(f12990,plain,
( spl0_739
<=> ! [X2,X0,X1] :
( null_class = intersection(cross_product(X0,X1),X2)
| regular(intersection(cross_product(X0,X1),X2)) = unordered_pair(unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),first(regular(intersection(cross_product(X0,X1),X2)))),unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),unordered_pair(second(regular(intersection(cross_product(X0,X1),X2))),second(regular(intersection(cross_product(X0,X1),X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f1029,plain,
( ! [X2,X0,X1] :
( null_class = intersection(cross_product(X0,X1),X2)
| regular(intersection(cross_product(X0,X1),X2)) = unordered_pair(unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),first(regular(intersection(cross_product(X0,X1),X2)))),unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),unordered_pair(second(regular(intersection(cross_product(X0,X1),X2))),second(regular(intersection(cross_product(X0,X1),X2)))))) )
| ~ spl0_79
| ~ spl0_128 ),
inference(resolution,[],[f1005,f629]) ).
fof(f12612,plain,
( spl0_738
| ~ spl0_9
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2027,f1998,f240,f12610]) ).
fof(f12610,plain,
( spl0_738
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(universal_class))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f2027,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(universal_class))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_9
| ~ spl0_212 ),
inference(resolution,[],[f1999,f241]) ).
fof(f12608,plain,
( spl0_737
| ~ spl0_9
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2004,f1994,f240,f12606]) ).
fof(f12606,plain,
( spl0_737
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(universal_class))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f2004,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(universal_class))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_9
| ~ spl0_211 ),
inference(resolution,[],[f1995,f241]) ).
fof(f12604,plain,
( spl0_736
| ~ spl0_20
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1894,f1868,f287,f12602]) ).
fof(f12602,plain,
( spl0_736
<=> ! [X2,X0,X1] :
( ~ subclass(composition_function,complement(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f1894,plain,
( ! [X2,X0,X1] :
( ~ subclass(composition_function,complement(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0) )
| ~ spl0_20
| ~ spl0_205 ),
inference(resolution,[],[f1869,f288]) ).
fof(f12600,plain,
( spl0_735
| spl0_150
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f1783,f1773,f1238,f12597]) ).
fof(f1238,plain,
( spl0_150
<=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f1783,plain,
( not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)))))
| spl0_150
| ~ spl0_200 ),
inference(resolution,[],[f1774,f1240]) ).
fof(f1240,plain,
( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
| spl0_150 ),
inference(avatar_component_clause,[],[f1238]) ).
fof(f12595,plain,
( spl0_734
| spl0_148
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f1782,f1773,f1229,f12592]) ).
fof(f1229,plain,
( spl0_148
<=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1782,plain,
( not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)))))
| spl0_148
| ~ spl0_200 ),
inference(resolution,[],[f1774,f1231]) ).
fof(f1231,plain,
( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
| spl0_148 ),
inference(avatar_component_clause,[],[f1229]) ).
fof(f12590,plain,
( spl0_733
| ~ spl0_137
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f1780,f1773,f1095,f12588]) ).
fof(f12588,plain,
( spl0_733
<=> ! [X0] :
( not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),second(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))))))
| cross_product(universal_class,universal_class) = compose_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f1095,plain,
( spl0_137
<=> ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
| cross_product(universal_class,universal_class) = compose_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1780,plain,
( ! [X0] :
( not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),second(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))))))
| cross_product(universal_class,universal_class) = compose_class(X0) )
| ~ spl0_137
| ~ spl0_200 ),
inference(resolution,[],[f1774,f1096]) ).
fof(f1096,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
| cross_product(universal_class,universal_class) = compose_class(X0) )
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1095]) ).
fof(f12196,plain,
( spl0_732
| ~ spl0_235
| ~ spl0_723 ),
inference(avatar_split_clause,[],[f12157,f12154,f2310,f12194]) ).
fof(f12194,plain,
( spl0_732
<=> ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation)
| null_class = X0
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f12154,plain,
( spl0_723
<=> ! [X0] :
( null_class = X0
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f12157,plain,
( ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation)
| null_class = X0
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_235
| ~ spl0_723 ),
inference(forward_demodulation,[],[f12155,f2312]) ).
fof(f12155,plain,
( ! [X0] :
( null_class = X0
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),identity_relation) )
| ~ spl0_723 ),
inference(avatar_component_clause,[],[f12154]) ).
fof(f12192,plain,
( spl0_731
| ~ spl0_235
| ~ spl0_722 ),
inference(avatar_split_clause,[],[f12152,f12149,f2310,f12190]) ).
fof(f12190,plain,
( spl0_731
<=> ! [X0] :
( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
| null_class = X0
| ~ member(X0,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f12149,plain,
( spl0_722
<=> ! [X0] :
( null_class = X0
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f12152,plain,
( ! [X0] :
( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
| null_class = X0
| ~ member(X0,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation) )
| ~ spl0_235
| ~ spl0_722 ),
inference(forward_demodulation,[],[f12150,f2312]) ).
fof(f12150,plain,
( ! [X0] :
( null_class = X0
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation) )
| ~ spl0_722 ),
inference(avatar_component_clause,[],[f12149]) ).
fof(f12188,plain,
( spl0_730
| ~ spl0_9
| ~ spl0_207 ),
inference(avatar_split_clause,[],[f1916,f1913,f240,f12186]) ).
fof(f12186,plain,
( spl0_730
<=> ! [X0,X1] :
( unordered_pair(X0,X1) = null_class
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f1913,plain,
( spl0_207
<=> ! [X0,X1] :
( ~ member(unordered_pair(X0,X1),universal_class)
| unordered_pair(X0,X1) = null_class
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f1916,plain,
( ! [X0,X1] :
( unordered_pair(X0,X1) = null_class
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
| ~ spl0_9
| ~ spl0_207 ),
inference(resolution,[],[f1914,f241]) ).
fof(f1914,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(X0,X1),universal_class)
| unordered_pair(X0,X1) = null_class
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
| ~ spl0_207 ),
inference(avatar_component_clause,[],[f1913]) ).
fof(f12184,plain,
( ~ spl0_729
| ~ spl0_235
| spl0_728 ),
inference(avatar_split_clause,[],[f12179,f12175,f2310,f12181]) ).
fof(f12181,plain,
( spl0_729
<=> subclass(composition_function,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f12175,plain,
( spl0_728
<=> subclass(composition_function,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f12179,plain,
( ~ subclass(composition_function,singleton_relation)
| ~ spl0_235
| spl0_728 ),
inference(forward_demodulation,[],[f12177,f2312]) ).
fof(f12177,plain,
( ~ subclass(composition_function,identity_relation)
| spl0_728 ),
inference(avatar_component_clause,[],[f12175]) ).
fof(f12178,plain,
( spl0_727
| ~ spl0_728
| ~ spl0_103
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1902,f1868,f761,f12175,f12172]) ).
fof(f12172,plain,
( spl0_727
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f1902,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,identity_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation) )
| ~ spl0_103
| ~ spl0_205 ),
inference(resolution,[],[f1869,f762]) ).
fof(f12170,plain,
( spl0_726
| ~ spl0_341
| ~ spl0_603 ),
inference(avatar_split_clause,[],[f11987,f9139,f3477,f12167]) ).
fof(f12167,plain,
( spl0_726
<=> null_class = intersection(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f11987,plain,
( null_class = intersection(null_class,universal_class)
| ~ spl0_341
| ~ spl0_603 ),
inference(superposition,[],[f9140,f3479]) ).
fof(f12165,plain,
( spl0_725
| ~ spl0_160
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1741,f1711,f1316,f12163]) ).
fof(f12163,plain,
( spl0_725
<=> ! [X0,X1] :
( unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = regular(regular(cross_product(X0,X1)))
| unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = regular(regular(cross_product(X0,X1)))
| null_class = regular(cross_product(X0,X1))
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f1316,plain,
( spl0_160
<=> ! [X0,X1] :
( regular(unordered_pair(X0,X1)) = X0
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1741,plain,
( ! [X0,X1] :
( unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = regular(regular(cross_product(X0,X1)))
| unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = regular(regular(cross_product(X0,X1)))
| null_class = regular(cross_product(X0,X1))
| cross_product(X0,X1) = null_class )
| ~ spl0_160
| ~ spl0_198 ),
inference(superposition,[],[f1317,f1712]) ).
fof(f1317,plain,
( ! [X0,X1] :
( regular(unordered_pair(X0,X1)) = X1
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class )
| ~ spl0_160 ),
inference(avatar_component_clause,[],[f1316]) ).
fof(f12161,plain,
( spl0_724
| ~ spl0_142
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1636,f1620,f1159,f12159]) ).
fof(f12159,plain,
( spl0_724
<=> ! [X0,X1] :
( null_class = X0
| ~ subclass(X0,regular(X1))
| ~ member(X0,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),null_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f1636,plain,
( ! [X0,X1] :
( null_class = X0
| ~ subclass(X0,regular(X1))
| ~ member(X0,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),null_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
| null_class = X1 )
| ~ spl0_142
| ~ spl0_193 ),
inference(resolution,[],[f1621,f1160]) ).
fof(f12156,plain,
( spl0_723
| ~ spl0_144
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1633,f1620,f1167,f12154]) ).
fof(f1633,plain,
( ! [X0] :
( null_class = X0
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),identity_relation) )
| ~ spl0_144
| ~ spl0_193 ),
inference(resolution,[],[f1621,f1168]) ).
fof(f12151,plain,
( spl0_722
| ~ spl0_143
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1630,f1620,f1163,f12149]) ).
fof(f1630,plain,
( ! [X0] :
( null_class = X0
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation) )
| ~ spl0_143
| ~ spl0_193 ),
inference(resolution,[],[f1621,f1164]) ).
fof(f12109,plain,
( spl0_721
| ~ spl0_39
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f1788,f1773,f376,f12107]) ).
fof(f12107,plain,
( spl0_721
<=> ! [X2,X0,X1] :
( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
| ~ subclass(X2,cross_product(X0,X1))
| cross_product(X0,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f1788,plain,
( ! [X2,X0,X1] :
( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
| ~ subclass(X2,cross_product(X0,X1))
| cross_product(X0,X1) = X2 )
| ~ spl0_39
| ~ spl0_200 ),
inference(resolution,[],[f1774,f377]) ).
fof(f12105,plain,
( spl0_720
| ~ spl0_89
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1754,f1745,f682,f12103]) ).
fof(f12103,plain,
( spl0_720
<=> ! [X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),compose(X3,X4))
| ~ operation(X2)
| member(not_homomorphism2(X0,X1,X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f1754,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),compose(X3,X4))
| ~ operation(X2)
| member(not_homomorphism2(X0,X1,X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))) )
| ~ spl0_89
| ~ spl0_199 ),
inference(resolution,[],[f1746,f683]) ).
fof(f12101,plain,
( spl0_719
| ~ spl0_94
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f881,f823,f718,f12099]) ).
fof(f12099,plain,
( spl0_719
<=> ! [X0] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),subset_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f718,plain,
( spl0_94
<=> ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f881,plain,
( ! [X0] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),subset_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) )
| ~ spl0_94
| ~ spl0_111 ),
inference(resolution,[],[f824,f719]) ).
fof(f719,plain,
( ! [X0] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f11902,plain,
( spl0_718
| ~ spl0_50
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1838,f1803,f452,f11900]) ).
fof(f11900,plain,
( spl0_718
<=> ! [X0,X3,X2,X1] :
( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),universal_class)))))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),compose(X2,X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f1838,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),universal_class)))))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),compose(X2,X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) )
| ~ spl0_50
| ~ spl0_202 ),
inference(superposition,[],[f1804,f453]) ).
fof(f11898,plain,
( spl0_717
| ~ spl0_132
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1740,f1711,f1020,f11896]) ).
fof(f11896,plain,
( spl0_717
<=> ! [X2,X0,X1] :
( ~ subclass(regular(cross_product(X0,X1)),X2)
| member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),X2)
| ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f1020,plain,
( spl0_132
<=> ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X1,X2)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1740,plain,
( ! [X2,X0,X1] :
( ~ subclass(regular(cross_product(X0,X1)),X2)
| member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),X2)
| ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
| cross_product(X0,X1) = null_class )
| ~ spl0_132
| ~ spl0_198 ),
inference(superposition,[],[f1021,f1712]) ).
fof(f1021,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X1,X2)
| ~ member(X1,universal_class) )
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1020]) ).
fof(f11894,plain,
( spl0_716
| ~ spl0_48
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1624,f1620,f444,f11892]) ).
fof(f11892,plain,
( spl0_716
<=> ! [X2,X0,X1] :
( null_class = X0
| ~ subclass(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f1624,plain,
( ! [X2,X0,X1] :
( null_class = X0
| ~ subclass(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X2 )
| ~ spl0_48
| ~ spl0_193 ),
inference(resolution,[],[f1621,f445]) ).
fof(f11865,plain,
( spl0_715
| ~ spl0_50
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f1799,f1793,f452,f11863]) ).
fof(f11863,plain,
( spl0_715
<=> ! [X2,X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f1799,plain,
( ! [X2,X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) )
| ~ spl0_50
| ~ spl0_201 ),
inference(superposition,[],[f1794,f453]) ).
fof(f11789,plain,
( spl0_714
| ~ spl0_50
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f1796,f1793,f452,f11787]) ).
fof(f11787,plain,
( spl0_714
<=> ! [X2,X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f1796,plain,
( ! [X2,X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) )
| ~ spl0_50
| ~ spl0_201 ),
inference(superposition,[],[f1794,f453]) ).
fof(f11785,plain,
( spl0_713
| ~ spl0_89
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1724,f1711,f682,f11783]) ).
fof(f11783,plain,
( spl0_713
<=> ! [X0,X3,X2,X1] :
( ~ member(regular(cross_product(X0,X1)),compose(X2,X3))
| member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))))
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f1724,plain,
( ! [X2,X3,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),compose(X2,X3))
| member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))))
| cross_product(X0,X1) = null_class )
| ~ spl0_89
| ~ spl0_198 ),
inference(superposition,[],[f683,f1712]) ).
fof(f11757,plain,
( spl0_712
| ~ spl0_77
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1933,f1923,f613,f11755]) ).
fof(f11755,plain,
( spl0_712
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X1,universal_class)
| null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f1933,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X1,universal_class)
| null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ member(X0,universal_class) )
| ~ spl0_77
| ~ spl0_208 ),
inference(duplicate_literal_removal,[],[f1926]) ).
fof(f1926,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X1,universal_class)
| null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_77
| ~ spl0_208 ),
inference(resolution,[],[f1924,f614]) ).
fof(f11753,plain,
( spl0_711
| ~ spl0_136
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f1776,f1773,f1091,f11751]) ).
fof(f11751,plain,
( spl0_711
<=> ! [X0] :
( not_subclass_element(cross_product(universal_class,universal_class),X0) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),first(not_subclass_element(cross_product(universal_class,universal_class),X0))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),X0)),second(not_subclass_element(cross_product(universal_class,universal_class),X0)))))
| cross_product(universal_class,universal_class) = X0
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f1091,plain,
( spl0_136
<=> ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| cross_product(universal_class,universal_class) = X0
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1776,plain,
( ! [X0] :
( not_subclass_element(cross_product(universal_class,universal_class),X0) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),first(not_subclass_element(cross_product(universal_class,universal_class),X0))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),X0)),second(not_subclass_element(cross_product(universal_class,universal_class),X0)))))
| cross_product(universal_class,universal_class) = X0
| ~ function(X0) )
| ~ spl0_136
| ~ spl0_200 ),
inference(resolution,[],[f1774,f1092]) ).
fof(f1092,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| cross_product(universal_class,universal_class) = X0
| ~ function(X0) )
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1091]) ).
fof(f11739,plain,
( spl0_710
| ~ spl0_30
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1735,f1711,f331,f11737]) ).
fof(f11737,plain,
( spl0_710
<=> ! [X0,X1] :
( member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),regular(cross_product(X0,X1)))
| ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f1735,plain,
( ! [X0,X1] :
( member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),regular(cross_product(X0,X1)))
| ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
| cross_product(X0,X1) = null_class )
| ~ spl0_30
| ~ spl0_198 ),
inference(superposition,[],[f332,f1712]) ).
fof(f11735,plain,
( ~ spl0_708
| spl0_709
| ~ spl0_165
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1568,f1556,f1369,f11733,f11729]) ).
fof(f11729,plain,
( spl0_708
<=> subclass(domain_relation,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f11733,plain,
( spl0_709
<=> ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation)
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f1568,plain,
( ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),cross_product(universal_class,universal_class))
| ~ subclass(domain_relation,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,universal_class) )
| ~ spl0_165
| ~ spl0_185 ),
inference(resolution,[],[f1557,f1370]) ).
fof(f11652,plain,
( spl0_707
| ~ spl0_38
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1757,f1745,f372,f11650]) ).
fof(f11650,plain,
( spl0_707
<=> ! [X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),X3)
| ~ operation(X2)
| ~ subclass(X3,X4)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f1757,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),X3)
| ~ operation(X2)
| ~ subclass(X3,X4)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X4) )
| ~ spl0_38
| ~ spl0_199 ),
inference(resolution,[],[f1746,f373]) ).
fof(f11646,plain,
( ~ spl0_706
| ~ spl0_235
| spl0_704 ),
inference(avatar_split_clause,[],[f11641,f11633,f2310,f11643]) ).
fof(f11643,plain,
( spl0_706
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f11633,plain,
( spl0_704
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f11641,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),singleton_relation)
| ~ spl0_235
| spl0_704 ),
inference(forward_demodulation,[],[f11635,f2312]) ).
fof(f11635,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation)
| spl0_704 ),
inference(avatar_component_clause,[],[f11633]) ).
fof(f11640,plain,
( ~ spl0_704
| ~ spl0_705
| spl0_430
| ~ spl0_125
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f1651,f1639,f959,f5490,f11637,f11633]) ).
fof(f11637,plain,
( spl0_705
<=> member(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f5490,plain,
( spl0_430
<=> null_class = complement(domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f1651,plain,
( null_class = complement(domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation)
| ~ spl0_125
| ~ spl0_194 ),
inference(resolution,[],[f1640,f960]) ).
fof(f11629,plain,
( ~ spl0_703
| ~ spl0_235
| spl0_700 ),
inference(avatar_split_clause,[],[f11609,f11600,f2310,f11626]) ).
fof(f11626,plain,
( spl0_703
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(compose(element_relation,complement(singleton_relation)))),complement(complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f11600,plain,
( spl0_700
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(compose(element_relation,complement(identity_relation)))),complement(complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f11609,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(compose(element_relation,complement(singleton_relation)))),complement(complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),singleton_relation)
| ~ spl0_235
| spl0_700 ),
inference(forward_demodulation,[],[f11602,f2312]) ).
fof(f11602,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(compose(element_relation,complement(identity_relation)))),complement(complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation)
| spl0_700 ),
inference(avatar_component_clause,[],[f11600]) ).
fof(f11624,plain,
( ~ spl0_702
| ~ spl0_235
| spl0_701 ),
inference(avatar_split_clause,[],[f11608,f11604,f2310,f11621]) ).
fof(f11621,plain,
( spl0_702
<=> member(complement(complement(compose(element_relation,complement(singleton_relation)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f11604,plain,
( spl0_701
<=> member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f11608,plain,
( ~ member(complement(complement(compose(element_relation,complement(singleton_relation)))),universal_class)
| ~ spl0_235
| spl0_701 ),
inference(forward_demodulation,[],[f11606,f2312]) ).
fof(f11606,plain,
( ~ member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class)
| spl0_701 ),
inference(avatar_component_clause,[],[f11604]) ).
fof(f11607,plain,
( ~ spl0_700
| ~ spl0_701
| spl0_425
| ~ spl0_124
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f1649,f1639,f955,f5463,f11604,f11600]) ).
fof(f5463,plain,
( spl0_425
<=> null_class = complement(complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f1649,plain,
( null_class = complement(complement(compose(element_relation,complement(identity_relation))))
| ~ member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(compose(element_relation,complement(identity_relation)))),complement(complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation)
| ~ spl0_124
| ~ spl0_194 ),
inference(resolution,[],[f1640,f956]) ).
fof(f11573,plain,
( spl0_699
| ~ spl0_31
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1761,f1745,f335,f11571]) ).
fof(f11571,plain,
( spl0_699
<=> ! [X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),intersection(X3,X4))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f1761,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),intersection(X3,X4))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3) )
| ~ spl0_31
| ~ spl0_199 ),
inference(resolution,[],[f1746,f336]) ).
fof(f11569,plain,
( spl0_698
| ~ spl0_32
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1760,f1745,f339,f11567]) ).
fof(f11567,plain,
( spl0_698
<=> ! [X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),intersection(X3,X4))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f1760,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),intersection(X3,X4))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X4) )
| ~ spl0_32
| ~ spl0_199 ),
inference(resolution,[],[f1746,f340]) ).
fof(f11476,plain,
( spl0_697
| ~ spl0_20
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1763,f1745,f287,f11474]) ).
fof(f11474,plain,
( spl0_697
<=> ! [X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),complement(X3))
| ~ operation(X2)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f1763,plain,
( ! [X2,X3,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),complement(X3))
| ~ operation(X2)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3) )
| ~ spl0_20
| ~ spl0_199 ),
inference(resolution,[],[f1746,f288]) ).
fof(f11472,plain,
( spl0_696
| ~ spl0_48
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1736,f1711,f444,f11470]) ).
fof(f11470,plain,
( spl0_696
<=> ! [X2,X0,X1] :
( ~ member(X2,regular(cross_product(X0,X1)))
| unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = X2
| unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = X2
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f1736,plain,
( ! [X2,X0,X1] :
( ~ member(X2,regular(cross_product(X0,X1)))
| unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = X2
| unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = X2
| cross_product(X0,X1) = null_class )
| ~ spl0_48
| ~ spl0_198 ),
inference(superposition,[],[f445,f1712]) ).
fof(f11453,plain,
( spl0_695
| ~ spl0_97
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1771,f1745,f731,f11451]) ).
fof(f11451,plain,
( spl0_695
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),singleton_relation)
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f1771,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),singleton_relation)
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation) )
| ~ spl0_97
| ~ spl0_199 ),
inference(resolution,[],[f1746,f732]) ).
fof(f11448,plain,
( spl0_694
| ~ spl0_103
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1769,f1745,f761,f11446]) ).
fof(f11446,plain,
( spl0_694
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),identity_relation)
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f1769,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),identity_relation)
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) )
| ~ spl0_103
| ~ spl0_199 ),
inference(resolution,[],[f1746,f762]) ).
fof(f11444,plain,
( spl0_693
| ~ spl0_126
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1738,f1711,f963,f11442]) ).
fof(f11442,plain,
( spl0_693
<=> ! [X0,X1] :
( ~ inductive(regular(cross_product(X0,X1)))
| null_class = unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))
| null_class = unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f963,plain,
( spl0_126
<=> ! [X0,X1] :
( null_class = X0
| null_class = X1
| ~ inductive(unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1738,plain,
( ! [X0,X1] :
( ~ inductive(regular(cross_product(X0,X1)))
| null_class = unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))
| null_class = unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = null_class )
| ~ spl0_126
| ~ spl0_198 ),
inference(superposition,[],[f964,f1712]) ).
fof(f964,plain,
( ! [X0,X1] :
( ~ inductive(unordered_pair(X0,X1))
| null_class = X1
| null_class = X0 )
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f963]) ).
fof(f11041,plain,
( spl0_692
| ~ spl0_38
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1709,f1704,f372,f11039]) ).
fof(f11039,plain,
( spl0_692
<=> ! [X0,X1] :
( ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
| ~ member(X0,universal_class)
| ~ subclass(successor_relation,X1)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f1709,plain,
( ! [X0,X1] :
( ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
| ~ member(X0,universal_class)
| ~ subclass(successor_relation,X1)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),X1) )
| ~ spl0_38
| ~ spl0_197 ),
inference(resolution,[],[f1705,f373]) ).
fof(f11037,plain,
( spl0_691
| ~ spl0_31
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1687,f1660,f335,f11035]) ).
fof(f11035,plain,
( spl0_691
<=> ! [X2,X0,X1] :
( null_class = intersection(intersection(X0,X1),X2)
| ~ member(intersection(intersection(X0,X1),X2),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f1687,plain,
( ! [X2,X0,X1] :
( null_class = intersection(intersection(X0,X1),X2)
| ~ member(intersection(intersection(X0,X1),X2),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X0) )
| ~ spl0_31
| ~ spl0_196 ),
inference(resolution,[],[f1661,f336]) ).
fof(f11033,plain,
( spl0_690
| ~ spl0_32
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1686,f1660,f339,f11031]) ).
fof(f11031,plain,
( spl0_690
<=> ! [X2,X0,X1] :
( null_class = intersection(intersection(X0,X1),X2)
| ~ member(intersection(intersection(X0,X1),X2),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f1686,plain,
( ! [X2,X0,X1] :
( null_class = intersection(intersection(X0,X1),X2)
| ~ member(intersection(intersection(X0,X1),X2),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X1) )
| ~ spl0_32
| ~ spl0_196 ),
inference(resolution,[],[f1661,f340]) ).
fof(f11029,plain,
( spl0_689
| ~ spl0_31
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f1667,f1656,f335,f11027]) ).
fof(f11027,plain,
( spl0_689
<=> ! [X2,X0,X1] :
( null_class = intersection(X0,intersection(X1,X2))
| ~ member(intersection(X0,intersection(X1,X2)),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f1667,plain,
( ! [X2,X0,X1] :
( null_class = intersection(X0,intersection(X1,X2))
| ~ member(intersection(X0,intersection(X1,X2)),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X1) )
| ~ spl0_31
| ~ spl0_195 ),
inference(resolution,[],[f1657,f336]) ).
fof(f11025,plain,
( spl0_688
| ~ spl0_32
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f1666,f1656,f339,f11023]) ).
fof(f11023,plain,
( spl0_688
<=> ! [X2,X0,X1] :
( null_class = intersection(X0,intersection(X1,X2))
| ~ member(intersection(X0,intersection(X1,X2)),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f1666,plain,
( ! [X2,X0,X1] :
( null_class = intersection(X0,intersection(X1,X2))
| ~ member(intersection(X0,intersection(X1,X2)),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X2) )
| ~ spl0_32
| ~ spl0_195 ),
inference(resolution,[],[f1657,f340]) ).
fof(f11021,plain,
( spl0_687
| ~ spl0_50
| ~ spl0_70
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1408,f1365,f568,f452,f11019]) ).
fof(f11019,plain,
( spl0_687
<=> ! [X2,X0,X1] :
( null_class = intersection(X2,cross_product(unordered_pair(not_subclass_element(X0,intersection(X1,domain_of(X2))),not_subclass_element(X0,intersection(X1,domain_of(X2)))),universal_class))
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),X1)
| subclass(X0,intersection(X1,domain_of(X2)))
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f1408,plain,
( ! [X2,X0,X1] :
( null_class = intersection(X2,cross_product(unordered_pair(not_subclass_element(X0,intersection(X1,domain_of(X2))),not_subclass_element(X0,intersection(X1,domain_of(X2)))),universal_class))
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),X1)
| subclass(X0,intersection(X1,domain_of(X2)))
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),universal_class) )
| ~ spl0_50
| ~ spl0_70
| ~ spl0_164 ),
inference(forward_demodulation,[],[f1395,f453]) ).
fof(f1395,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),X1)
| subclass(X0,intersection(X1,domain_of(X2)))
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),universal_class)
| null_class = intersection(cross_product(unordered_pair(not_subclass_element(X0,intersection(X1,domain_of(X2))),not_subclass_element(X0,intersection(X1,domain_of(X2)))),universal_class),X2) )
| ~ spl0_70
| ~ spl0_164 ),
inference(resolution,[],[f1366,f569]) ).
fof(f10795,plain,
( spl0_686
| spl0_122
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f1781,f1773,f946,f10792]) ).
fof(f946,plain,
( spl0_122
<=> subclass(cross_product(universal_class,universal_class),domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1781,plain,
( not_subclass_element(cross_product(universal_class,universal_class),domain_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)))))
| spl0_122
| ~ spl0_200 ),
inference(resolution,[],[f1774,f948]) ).
fof(f948,plain,
( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
| spl0_122 ),
inference(avatar_component_clause,[],[f946]) ).
fof(f10790,plain,
( spl0_685
| ~ spl0_234
| ~ spl0_235
| ~ spl0_569 ),
inference(avatar_split_clause,[],[f10436,f8667,f2310,f2304,f10787]) ).
fof(f10787,plain,
( spl0_685
<=> member(regular(singleton_relation),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f8667,plain,
( spl0_569
<=> ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f10436,plain,
( member(regular(singleton_relation),universal_class)
| ~ spl0_234
| ~ spl0_235
| ~ spl0_569 ),
inference(forward_demodulation,[],[f10377,f2312]) ).
fof(f10377,plain,
( member(regular(identity_relation),universal_class)
| ~ spl0_234
| ~ spl0_569 ),
inference(resolution,[],[f8668,f2306]) ).
fof(f8668,plain,
( ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,universal_class) )
| ~ spl0_569 ),
inference(avatar_component_clause,[],[f8667]) ).
fof(f10785,plain,
( spl0_684
| spl0_120
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f1778,f1773,f936,f10782]) ).
fof(f936,plain,
( spl0_120
<=> subclass(cross_product(universal_class,universal_class),successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1778,plain,
( not_subclass_element(cross_product(universal_class,universal_class),successor_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)))))
| spl0_120
| ~ spl0_200 ),
inference(resolution,[],[f1774,f938]) ).
fof(f938,plain,
( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
| spl0_120 ),
inference(avatar_component_clause,[],[f936]) ).
fof(f10780,plain,
( spl0_683
| spl0_118
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f1777,f1773,f927,f10777]) ).
fof(f927,plain,
( spl0_118
<=> subclass(cross_product(universal_class,universal_class),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1777,plain,
( not_subclass_element(cross_product(universal_class,universal_class),element_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),element_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)))))
| spl0_118
| ~ spl0_200 ),
inference(resolution,[],[f1774,f929]) ).
fof(f929,plain,
( ~ subclass(cross_product(universal_class,universal_class),element_relation)
| spl0_118 ),
inference(avatar_component_clause,[],[f927]) ).
fof(f10603,plain,
( spl0_682
| ~ spl0_152
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1312,f1294,f1247,f10601]) ).
fof(f10601,plain,
( spl0_682
<=> ! [X0] :
( null_class = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class)
| ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f1312,plain,
( ! [X0] :
( null_class = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class)
| ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class))))
| ~ member(X0,universal_class) )
| ~ spl0_152
| ~ spl0_158 ),
inference(resolution,[],[f1295,f1248]) ).
fof(f10599,plain,
( spl0_681
| ~ spl0_96
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f842,f802,f727,f10597]) ).
fof(f842,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,flip(X0))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) )
| ~ spl0_96
| ~ spl0_106 ),
inference(resolution,[],[f803,f728]) ).
fof(f10595,plain,
( spl0_680
| ~ spl0_95
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f841,f802,f723,f10593]) ).
fof(f841,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,rotate(X0))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) )
| ~ spl0_95
| ~ spl0_106 ),
inference(resolution,[],[f803,f724]) ).
fof(f10562,plain,
( spl0_678
| ~ spl0_679
| ~ spl0_78
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1880,f1868,f624,f10559,f10556]) ).
fof(f10556,plain,
( spl0_678
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f10559,plain,
( spl0_679
<=> subclass(composition_function,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f624,plain,
( spl0_78
<=> ! [X0,X1] :
( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1880,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) )
| ~ spl0_78
| ~ spl0_205 ),
inference(resolution,[],[f1869,f625]) ).
fof(f625,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
| complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 )
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f624]) ).
fof(f10554,plain,
( spl0_677
| ~ spl0_78
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1753,f1745,f624,f10552]) ).
fof(f10552,plain,
( spl0_677
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),successor_relation)
| ~ operation(X2)
| not_homomorphism2(X0,X1,X2) = complement(intersection(complement(not_homomorphism1(X0,X1,X2)),complement(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f1753,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),successor_relation)
| ~ operation(X2)
| not_homomorphism2(X0,X1,X2) = complement(intersection(complement(not_homomorphism1(X0,X1,X2)),complement(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2))))) )
| ~ spl0_78
| ~ spl0_199 ),
inference(resolution,[],[f1746,f625]) ).
fof(f10550,plain,
( spl0_676
| ~ spl0_142
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1510,f1456,f1159,f10548]) ).
fof(f10548,plain,
( spl0_676
<=> ! [X0,X1] :
( ~ subclass(universal_class,regular(X0))
| ~ member(X1,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),null_class)
| ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f1510,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,regular(X0))
| ~ member(X1,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),null_class)
| ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0)
| null_class = X0 )
| ~ spl0_142
| ~ spl0_171 ),
inference(resolution,[],[f1457,f1160]) ).
fof(f10546,plain,
( spl0_675
| ~ spl0_435
| ~ spl0_143
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1504,f1456,f1163,f5514,f10544]) ).
fof(f10544,plain,
( spl0_675
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),singleton_relation)
| ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f5514,plain,
( spl0_435
<=> subclass(universal_class,complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f1504,plain,
( ! [X0] :
( ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,universal_class)
| ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),element_relation)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),singleton_relation) )
| ~ spl0_143
| ~ spl0_171 ),
inference(resolution,[],[f1457,f1164]) ).
fof(f10446,plain,
( spl0_674
| ~ spl0_131
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1739,f1711,f1016,f10444]) ).
fof(f10444,plain,
( spl0_674
<=> ! [X2,X0,X1] :
( ~ subclass(regular(cross_product(X0,X1)),X2)
| member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),X2)
| ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f1016,plain,
( spl0_131
<=> ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1739,plain,
( ! [X2,X0,X1] :
( ~ subclass(regular(cross_product(X0,X1)),X2)
| member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),X2)
| ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| cross_product(X0,X1) = null_class )
| ~ spl0_131
| ~ spl0_198 ),
inference(superposition,[],[f1017,f1712]) ).
fof(f1017,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,universal_class) )
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f1016]) ).
fof(f10442,plain,
( spl0_673
| ~ spl0_78
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1720,f1711,f624,f10440]) ).
fof(f10440,plain,
( spl0_673
<=> ! [X0,X1] :
( ~ member(regular(cross_product(X0,X1)),successor_relation)
| second(regular(cross_product(X0,X1))) = complement(intersection(complement(first(regular(cross_product(X0,X1)))),complement(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))))
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f1720,plain,
( ! [X0,X1] :
( ~ member(regular(cross_product(X0,X1)),successor_relation)
| second(regular(cross_product(X0,X1))) = complement(intersection(complement(first(regular(cross_product(X0,X1)))),complement(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))))
| cross_product(X0,X1) = null_class )
| ~ spl0_78
| ~ spl0_198 ),
inference(superposition,[],[f625,f1712]) ).
fof(f10373,plain,
( spl0_672
| ~ spl0_20
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1689,f1660,f287,f10371]) ).
fof(f10371,plain,
( spl0_672
<=> ! [X0,X1] :
( null_class = intersection(complement(X0),X1)
| ~ member(intersection(complement(X0),X1),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(X0),X1),intersection(complement(X0),X1)),universal_class)),universal_class))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f1689,plain,
( ! [X0,X1] :
( null_class = intersection(complement(X0),X1)
| ~ member(intersection(complement(X0),X1),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(X0),X1),intersection(complement(X0),X1)),universal_class)),universal_class))))))),X0) )
| ~ spl0_20
| ~ spl0_196 ),
inference(resolution,[],[f1661,f288]) ).
fof(f10369,plain,
( spl0_671
| ~ spl0_20
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f1669,f1656,f287,f10367]) ).
fof(f10367,plain,
( spl0_671
<=> ! [X0,X1] :
( null_class = intersection(X0,complement(X1))
| ~ member(intersection(X0,complement(X1)),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(X1)),intersection(X0,complement(X1))),universal_class)),universal_class))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f1669,plain,
( ! [X0,X1] :
( null_class = intersection(X0,complement(X1))
| ~ member(intersection(X0,complement(X1)),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(X1)),intersection(X0,complement(X1))),universal_class)),universal_class))))))),X1) )
| ~ spl0_20
| ~ spl0_195 ),
inference(resolution,[],[f1657,f288]) ).
fof(f10362,plain,
( ~ spl0_669
| ~ spl0_670
| spl0_344
| ~ spl0_111
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f1645,f1639,f823,f3490,f10359,f10355]) ).
fof(f10355,plain,
( spl0_669
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(cross_product(universal_class,universal_class)),complement(cross_product(universal_class,universal_class))),universal_class)),universal_class))))))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f10359,plain,
( spl0_670
<=> member(complement(cross_product(universal_class,universal_class)),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f1645,plain,
( null_class = complement(cross_product(universal_class,universal_class))
| ~ member(complement(cross_product(universal_class,universal_class)),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(cross_product(universal_class,universal_class)),complement(cross_product(universal_class,universal_class))),universal_class)),universal_class))))))),subset_relation)
| ~ spl0_111
| ~ spl0_194 ),
inference(resolution,[],[f1640,f824]) ).
fof(f9980,plain,
( spl0_668
| ~ spl0_176
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1732,f1711,f1477,f9978]) ).
fof(f9978,plain,
( spl0_668
<=> ! [X0,X1] :
( member(regular(cross_product(X0,X1)),element_relation)
| ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
| ~ member(second(regular(cross_product(X0,X1))),universal_class)
| ~ member(first(regular(cross_product(X0,X1))),universal_class)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f1732,plain,
( ! [X0,X1] :
( member(regular(cross_product(X0,X1)),element_relation)
| ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
| ~ member(second(regular(cross_product(X0,X1))),universal_class)
| ~ member(first(regular(cross_product(X0,X1))),universal_class)
| cross_product(X0,X1) = null_class )
| ~ spl0_176
| ~ spl0_198 ),
inference(superposition,[],[f1478,f1712]) ).
fof(f9976,plain,
( spl0_667
| ~ spl0_113
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1691,f1660,f888,f9974]) ).
fof(f9974,plain,
( spl0_667
<=> ! [X0,X1] :
( null_class = intersection(null_class,X0)
| ~ member(intersection(null_class,X0),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(null_class,X0),intersection(null_class,X0)),universal_class)),universal_class))))))),X1)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f888,plain,
( spl0_113
<=> ! [X0,X1] :
( ~ member(X1,null_class)
| member(X1,X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f1691,plain,
( ! [X0,X1] :
( null_class = intersection(null_class,X0)
| ~ member(intersection(null_class,X0),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(null_class,X0),intersection(null_class,X0)),universal_class)),universal_class))))))),X1)
| null_class = X1 )
| ~ spl0_113
| ~ spl0_196 ),
inference(resolution,[],[f1661,f889]) ).
fof(f889,plain,
( ! [X0,X1] :
( ~ member(X1,null_class)
| member(X1,X0)
| null_class = X0 )
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f888]) ).
fof(f9972,plain,
( spl0_666
| ~ spl0_38
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1683,f1660,f372,f9970]) ).
fof(f9970,plain,
( spl0_666
<=> ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| ~ member(intersection(X0,X1),universal_class)
| ~ subclass(X0,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f1683,plain,
( ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| ~ member(intersection(X0,X1),universal_class)
| ~ subclass(X0,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) )
| ~ spl0_38
| ~ spl0_196 ),
inference(resolution,[],[f1661,f373]) ).
fof(f9968,plain,
( spl0_665
| ~ spl0_113
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f1671,f1656,f888,f9966]) ).
fof(f9966,plain,
( spl0_665
<=> ! [X0,X1] :
( null_class = intersection(X0,null_class)
| ~ member(intersection(X0,null_class),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,null_class),intersection(X0,null_class)),universal_class)),universal_class))))))),X1)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f1671,plain,
( ! [X0,X1] :
( null_class = intersection(X0,null_class)
| ~ member(intersection(X0,null_class),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,null_class),intersection(X0,null_class)),universal_class)),universal_class))))))),X1)
| null_class = X1 )
| ~ spl0_113
| ~ spl0_195 ),
inference(resolution,[],[f1657,f889]) ).
fof(f9964,plain,
( spl0_664
| ~ spl0_38
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f1663,f1656,f372,f9962]) ).
fof(f9962,plain,
( spl0_664
<=> ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| ~ member(intersection(X0,X1),universal_class)
| ~ subclass(X1,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f1663,plain,
( ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| ~ member(intersection(X0,X1),universal_class)
| ~ subclass(X1,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) )
| ~ spl0_38
| ~ spl0_195 ),
inference(resolution,[],[f1657,f373]) ).
fof(f9960,plain,
( spl0_663
| ~ spl0_123
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f1652,f1639,f951,f9958]) ).
fof(f9958,plain,
( spl0_663
<=> ! [X0] :
( null_class = complement(regular(X0))
| ~ member(complement(regular(X0)),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(regular(X0)),complement(regular(X0))),universal_class)),universal_class))))))),null_class)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f1652,plain,
( ! [X0] :
( null_class = complement(regular(X0))
| ~ member(complement(regular(X0)),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(regular(X0)),complement(regular(X0))),universal_class)),universal_class))))))),null_class)
| null_class = X0 )
| ~ spl0_123
| ~ spl0_194 ),
inference(resolution,[],[f1640,f952]) ).
fof(f9956,plain,
( spl0_662
| ~ spl0_48
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1499,f1456,f444,f9954]) ).
fof(f9954,plain,
( spl0_662
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| ~ member(X2,universal_class)
| complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X0
| complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f1499,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| ~ member(X2,universal_class)
| complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X0
| complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X1 )
| ~ spl0_48
| ~ spl0_171 ),
inference(resolution,[],[f1457,f445]) ).
fof(f9952,plain,
( spl0_661
| ~ spl0_142
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1492,f1452,f1159,f9950]) ).
fof(f9950,plain,
( spl0_661
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,regular(X1))
| ~ member(X2,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),null_class)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f1492,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,regular(X1))
| ~ member(X2,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),null_class)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
| null_class = X1 )
| ~ spl0_142
| ~ spl0_170 ),
inference(resolution,[],[f1453,f1160]) ).
fof(f9948,plain,
( ~ spl0_435
| spl0_660
| ~ spl0_143
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1486,f1452,f1163,f9946,f5514]) ).
fof(f9946,plain,
( spl0_660
<=> ! [X0,X1] :
( ~ function(X0)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),singleton_relation)
| ~ member(X1,universal_class)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f1486,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X1,universal_class)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),element_relation)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),singleton_relation) )
| ~ spl0_143
| ~ spl0_170 ),
inference(resolution,[],[f1453,f1164]) ).
fof(f9944,plain,
( spl0_659
| ~ spl0_142
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1434,f1369,f1159,f9942]) ).
fof(f9942,plain,
( spl0_659
<=> ! [X0,X1] :
( ~ subclass(domain_relation,regular(X0))
| ~ member(X1,universal_class)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),null_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f1434,plain,
( ! [X0,X1] :
( ~ subclass(domain_relation,regular(X0))
| ~ member(X1,universal_class)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),null_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0)
| null_class = X0 )
| ~ spl0_142
| ~ spl0_165 ),
inference(resolution,[],[f1370,f1160]) ).
fof(f9939,plain,
( spl0_657
| ~ spl0_658
| ~ spl0_144
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1431,f1369,f1167,f9936,f9933]) ).
fof(f9933,plain,
( spl0_657
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),identity_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f9936,plain,
( spl0_658
<=> subclass(domain_relation,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f1431,plain,
( ! [X0] :
( ~ subclass(domain_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),identity_relation) )
| ~ spl0_144
| ~ spl0_165 ),
inference(resolution,[],[f1370,f1168]) ).
fof(f9931,plain,
( ~ spl0_656
| ~ spl0_235
| spl0_655 ),
inference(avatar_split_clause,[],[f9926,f9922,f2310,f9928]) ).
fof(f9928,plain,
( spl0_656
<=> subclass(domain_relation,complement(compose(element_relation,complement(singleton_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f9922,plain,
( spl0_655
<=> subclass(domain_relation,complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f9926,plain,
( ~ subclass(domain_relation,complement(compose(element_relation,complement(singleton_relation))))
| ~ spl0_235
| spl0_655 ),
inference(forward_demodulation,[],[f9924,f2312]) ).
fof(f9924,plain,
( ~ subclass(domain_relation,complement(compose(element_relation,complement(identity_relation))))
| spl0_655 ),
inference(avatar_component_clause,[],[f9922]) ).
fof(f9925,plain,
( spl0_654
| ~ spl0_655
| ~ spl0_143
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1428,f1369,f1163,f9922,f9919]) ).
fof(f9919,plain,
( spl0_654
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),singleton_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f1428,plain,
( ! [X0] :
( ~ subclass(domain_relation,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),singleton_relation) )
| ~ spl0_143
| ~ spl0_165 ),
inference(resolution,[],[f1370,f1164]) ).
fof(f9917,plain,
( spl0_652
| ~ spl0_653
| ~ spl0_9
| ~ spl0_341
| ~ spl0_489 ),
inference(avatar_split_clause,[],[f6767,f6441,f3477,f240,f9914,f9911]) ).
fof(f9914,plain,
( spl0_653
<=> subclass(domain_relation,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f6767,plain,
( ! [X0] :
( ~ subclass(domain_relation,null_class)
| ~ member(X0,universal_class) )
| ~ spl0_9
| ~ spl0_341
| ~ spl0_489 ),
inference(forward_demodulation,[],[f6744,f3479]) ).
fof(f6744,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| ~ subclass(domain_relation,complement(universal_class)) )
| ~ spl0_9
| ~ spl0_489 ),
inference(resolution,[],[f6442,f241]) ).
fof(f9909,plain,
( spl0_651
| ~ spl0_79
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1063,f1012,f628,f9907]) ).
fof(f9907,plain,
( spl0_651
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,cross_product(X1,X2))
| subclass(X0,X3)
| not_subclass_element(X0,X3) = unordered_pair(unordered_pair(first(not_subclass_element(X0,X3)),first(not_subclass_element(X0,X3))),unordered_pair(first(not_subclass_element(X0,X3)),unordered_pair(second(not_subclass_element(X0,X3)),second(not_subclass_element(X0,X3))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f1063,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,cross_product(X1,X2))
| subclass(X0,X3)
| not_subclass_element(X0,X3) = unordered_pair(unordered_pair(first(not_subclass_element(X0,X3)),first(not_subclass_element(X0,X3))),unordered_pair(first(not_subclass_element(X0,X3)),unordered_pair(second(not_subclass_element(X0,X3)),second(not_subclass_element(X0,X3))))) )
| ~ spl0_79
| ~ spl0_130 ),
inference(resolution,[],[f1013,f629]) ).
fof(f9903,plain,
( spl0_650
| ~ spl0_87
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1723,f1711,f673,f9901]) ).
fof(f9901,plain,
( spl0_650
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),composition_function)
| second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f673,plain,
( spl0_87
<=> ! [X4,X0,X1] :
( compose(X0,X1) = X4
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1723,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),composition_function)
| second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = null_class )
| ~ spl0_87
| ~ spl0_198 ),
inference(superposition,[],[f674,f1712]) ).
fof(f674,plain,
( ! [X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function)
| compose(X0,X1) = X4 )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f673]) ).
fof(f9781,plain,
( spl0_649
| ~ spl0_72
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1882,f1868,f584,f9779]) ).
fof(f9779,plain,
( spl0_649
<=> ! [X2,X0,X1] :
( ~ subclass(composition_function,compose_class(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| compose(X0,X1) = unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f584,plain,
( spl0_72
<=> ! [X4,X0,X1] :
( compose(X0,X1) = X4
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f1882,plain,
( ! [X2,X0,X1] :
( ~ subclass(composition_function,compose_class(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| compose(X0,X1) = unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))) )
| ~ spl0_72
| ~ spl0_205 ),
inference(resolution,[],[f1869,f585]) ).
fof(f585,plain,
( ! [X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0))
| compose(X0,X1) = X4 )
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f584]) ).
fof(f9777,plain,
( spl0_648
| ~ spl0_29
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1734,f1711,f327,f9775]) ).
fof(f9775,plain,
( spl0_648
<=> ! [X0,X1] :
( member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),regular(cross_product(X0,X1)))
| ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f1734,plain,
( ! [X0,X1] :
( member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),regular(cross_product(X0,X1)))
| ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| cross_product(X0,X1) = null_class )
| ~ spl0_29
| ~ spl0_198 ),
inference(superposition,[],[f328,f1712]) ).
fof(f9773,plain,
( spl0_647
| ~ spl0_48
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1481,f1452,f444,f9771]) ).
fof(f9771,plain,
( spl0_647
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ subclass(universal_class,unordered_pair(X1,X2))
| ~ member(X3,universal_class)
| domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = X1
| domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f1481,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,unordered_pair(X1,X2))
| ~ member(X3,universal_class)
| domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = X1
| domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = X2 )
| ~ spl0_48
| ~ spl0_170 ),
inference(resolution,[],[f1453,f445]) ).
fof(f9769,plain,
( spl0_646
| ~ spl0_48
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1423,f1369,f444,f9767]) ).
fof(f9767,plain,
( spl0_646
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,unordered_pair(X0,X1))
| ~ member(X2,universal_class)
| unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))) = X0
| unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f1423,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,unordered_pair(X0,X1))
| ~ member(X2,universal_class)
| unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))) = X0
| unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))) = X1 )
| ~ spl0_48
| ~ spl0_165 ),
inference(resolution,[],[f1370,f445]) ).
fof(f9765,plain,
( spl0_645
| ~ spl0_49
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1391,f1365,f448,f9763]) ).
fof(f9763,plain,
( spl0_645
<=> ! [X0,X3,X2,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X1)
| subclass(X0,intersection(X1,intersection(X2,X3)))
| ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X3)
| ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f1391,plain,
( ! [X2,X3,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X1)
| subclass(X0,intersection(X1,intersection(X2,X3)))
| ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X3)
| ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X2) )
| ~ spl0_49
| ~ spl0_164 ),
inference(resolution,[],[f1366,f449]) ).
fof(f9761,plain,
( spl0_644
| ~ spl0_115
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1358,f1351,f915,f9759]) ).
fof(f9759,plain,
( spl0_644
<=> ! [X0] :
( ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation)
| subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f915,plain,
( spl0_115
<=> ! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f1358,plain,
( ! [X0] :
( ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation)
| subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) )
| ~ spl0_115
| ~ spl0_162 ),
inference(resolution,[],[f1352,f916]) ).
fof(f916,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(complement(X0),X1),X0)
| subclass(complement(X0),X1) )
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f915]) ).
fof(f9720,plain,
( spl0_643
| ~ spl0_235
| ~ spl0_637 ),
inference(avatar_split_clause,[],[f9687,f9682,f2310,f9718]) ).
fof(f9718,plain,
( spl0_643
<=> ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),subset_relation)
| ~ member(intersection(singleton_relation,X0),universal_class)
| null_class = intersection(singleton_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f9682,plain,
( spl0_637
<=> ! [X0] :
( null_class = intersection(identity_relation,X0)
| ~ member(intersection(identity_relation,X0),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f9687,plain,
( ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),subset_relation)
| ~ member(intersection(singleton_relation,X0),universal_class)
| null_class = intersection(singleton_relation,X0) )
| ~ spl0_235
| ~ spl0_637 ),
inference(forward_demodulation,[],[f9686,f2312]) ).
fof(f9686,plain,
( ! [X0] :
( ~ member(intersection(singleton_relation,X0),universal_class)
| null_class = intersection(singleton_relation,X0)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_235
| ~ spl0_637 ),
inference(forward_demodulation,[],[f9685,f2312]) ).
fof(f9685,plain,
( ! [X0] :
( null_class = intersection(singleton_relation,X0)
| ~ member(intersection(identity_relation,X0),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_235
| ~ spl0_637 ),
inference(forward_demodulation,[],[f9683,f2312]) ).
fof(f9683,plain,
( ! [X0] :
( null_class = intersection(identity_relation,X0)
| ~ member(intersection(identity_relation,X0),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_637 ),
inference(avatar_component_clause,[],[f9682]) ).
fof(f9716,plain,
( ~ spl0_641
| spl0_642
| ~ spl0_106
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f3839,f3753,f802,f9714,f9710]) ).
fof(f9710,plain,
( spl0_641
<=> subclass(universal_class,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f3753,plain,
( spl0_360
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f3839,plain,
( ! [X0] :
( member(X0,universal_class)
| ~ subclass(universal_class,subset_relation) )
| ~ spl0_106
| ~ spl0_360 ),
inference(resolution,[],[f3754,f803]) ).
fof(f3754,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(X0,universal_class) )
| ~ spl0_360 ),
inference(avatar_component_clause,[],[f3753]) ).
fof(f9699,plain,
( spl0_640
| ~ spl0_235
| ~ spl0_635 ),
inference(avatar_split_clause,[],[f9676,f9671,f2310,f9697]) ).
fof(f9697,plain,
( spl0_640
<=> ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),subset_relation)
| ~ member(intersection(X0,singleton_relation),universal_class)
| null_class = intersection(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f9671,plain,
( spl0_635
<=> ! [X0] :
( null_class = intersection(X0,identity_relation)
| ~ member(intersection(X0,identity_relation),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f9676,plain,
( ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),subset_relation)
| ~ member(intersection(X0,singleton_relation),universal_class)
| null_class = intersection(X0,singleton_relation) )
| ~ spl0_235
| ~ spl0_635 ),
inference(forward_demodulation,[],[f9675,f2312]) ).
fof(f9675,plain,
( ! [X0] :
( ~ member(intersection(X0,singleton_relation),universal_class)
| null_class = intersection(X0,singleton_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_235
| ~ spl0_635 ),
inference(forward_demodulation,[],[f9674,f2312]) ).
fof(f9674,plain,
( ! [X0] :
( null_class = intersection(X0,singleton_relation)
| ~ member(intersection(X0,identity_relation),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_235
| ~ spl0_635 ),
inference(forward_demodulation,[],[f9672,f2312]) ).
fof(f9672,plain,
( ! [X0] :
( null_class = intersection(X0,identity_relation)
| ~ member(intersection(X0,identity_relation),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_635 ),
inference(avatar_component_clause,[],[f9671]) ).
fof(f9695,plain,
( spl0_639
| ~ spl0_67
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1876,f1868,f556,f9693]) ).
fof(f9693,plain,
( spl0_639
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,cross_product(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f1876,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,cross_product(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),X1) )
| ~ spl0_67
| ~ spl0_205 ),
inference(resolution,[],[f1869,f557]) ).
fof(f9691,plain,
( spl0_638
| ~ spl0_97
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1696,f1660,f731,f9689]) ).
fof(f9689,plain,
( spl0_638
<=> ! [X0] :
( null_class = intersection(singleton_relation,X0)
| ~ member(intersection(singleton_relation,X0),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f1696,plain,
( ! [X0] :
( null_class = intersection(singleton_relation,X0)
| ~ member(intersection(singleton_relation,X0),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),element_relation) )
| ~ spl0_97
| ~ spl0_196 ),
inference(resolution,[],[f1661,f732]) ).
fof(f9684,plain,
( spl0_637
| ~ spl0_103
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1694,f1660,f761,f9682]) ).
fof(f1694,plain,
( ! [X0] :
( null_class = intersection(identity_relation,X0)
| ~ member(intersection(identity_relation,X0),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_103
| ~ spl0_196 ),
inference(resolution,[],[f1661,f762]) ).
fof(f9680,plain,
( spl0_636
| ~ spl0_97
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f1676,f1656,f731,f9678]) ).
fof(f9678,plain,
( spl0_636
<=> ! [X0] :
( null_class = intersection(X0,singleton_relation)
| ~ member(intersection(X0,singleton_relation),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f1676,plain,
( ! [X0] :
( null_class = intersection(X0,singleton_relation)
| ~ member(intersection(X0,singleton_relation),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),element_relation) )
| ~ spl0_97
| ~ spl0_195 ),
inference(resolution,[],[f1657,f732]) ).
fof(f9673,plain,
( spl0_635
| ~ spl0_103
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f1674,f1656,f761,f9671]) ).
fof(f1674,plain,
( ! [X0] :
( null_class = intersection(X0,identity_relation)
| ~ member(intersection(X0,identity_relation),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_103
| ~ spl0_195 ),
inference(resolution,[],[f1657,f762]) ).
fof(f9666,plain,
( spl0_633
| ~ spl0_634
| ~ spl0_112
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1359,f1351,f884,f9663,f9659]) ).
fof(f9663,plain,
( spl0_634
<=> member(regular(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f1359,plain,
( ~ member(regular(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
| null_class = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ spl0_112
| ~ spl0_162 ),
inference(resolution,[],[f1352,f885]) ).
fof(f9657,plain,
( spl0_632
| ~ spl0_4
| ~ spl0_357 ),
inference(avatar_split_clause,[],[f3738,f3595,f219,f9655]) ).
fof(f9655,plain,
( spl0_632
<=> ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f3595,plain,
( spl0_357
<=> ! [X0,X1] :
( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X1)
| ~ member(X0,singleton_relation)
| member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f3738,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,universal_class) )
| ~ spl0_4
| ~ spl0_357 ),
inference(resolution,[],[f3596,f220]) ).
fof(f3596,plain,
( ! [X0,X1] :
( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X1)
| ~ member(X0,singleton_relation)
| member(X0,X1) )
| ~ spl0_357 ),
inference(avatar_component_clause,[],[f3595]) ).
fof(f9583,plain,
( spl0_630
| spl0_631
| ~ spl0_79
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f847,f802,f628,f9581,f9578]) ).
fof(f9578,plain,
( spl0_630
<=> ! [X2,X3] : unordered_pair(X2,X3) = unordered_pair(unordered_pair(first(unordered_pair(X2,X3)),first(unordered_pair(X2,X3))),unordered_pair(first(unordered_pair(X2,X3)),unordered_pair(second(unordered_pair(X2,X3)),second(unordered_pair(X2,X3))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f847,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| unordered_pair(X2,X3) = unordered_pair(unordered_pair(first(unordered_pair(X2,X3)),first(unordered_pair(X2,X3))),unordered_pair(first(unordered_pair(X2,X3)),unordered_pair(second(unordered_pair(X2,X3)),second(unordered_pair(X2,X3))))) )
| ~ spl0_79
| ~ spl0_106 ),
inference(resolution,[],[f803,f629]) ).
fof(f9527,plain,
( spl0_628
| ~ spl0_629
| ~ spl0_64
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1883,f1868,f539,f9524,f9521]) ).
fof(f9521,plain,
( spl0_628
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| domain_of(X0) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f9524,plain,
( spl0_629
<=> subclass(composition_function,domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f539,plain,
( spl0_64
<=> ! [X0,X1] :
( domain_of(X0) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1883,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,domain_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| domain_of(X0) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) )
| ~ spl0_64
| ~ spl0_205 ),
inference(resolution,[],[f1869,f540]) ).
fof(f540,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation)
| domain_of(X0) = X1 )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f539]) ).
fof(f9519,plain,
( spl0_627
| ~ spl0_89
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1415,f1369,f682,f9517]) ).
fof(f9517,plain,
( spl0_627
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,compose(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f1415,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,compose(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) )
| ~ spl0_89
| ~ spl0_165 ),
inference(resolution,[],[f1370,f683]) ).
fof(f9515,plain,
( spl0_626
| ~ spl0_28
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1357,f1351,f323,f9513]) ).
fof(f9513,plain,
( spl0_626
<=> ! [X0] :
( ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
| subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f1357,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
| subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
| ~ spl0_28
| ~ spl0_162 ),
inference(resolution,[],[f1352,f324]) ).
fof(f9457,plain,
( spl0_625
| ~ spl0_235
| ~ spl0_293
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f3673,f3529,f2822,f2310,f9454]) ).
fof(f9454,plain,
( spl0_625
<=> null_class = intersection(singleton_relation,complement(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f2822,plain,
( spl0_293
<=> ! [X0] :
( null_class = intersection(identity_relation,X0)
| member(regular(intersection(identity_relation,X0)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f3673,plain,
( null_class = intersection(singleton_relation,complement(subset_relation))
| ~ spl0_235
| ~ spl0_293
| ~ spl0_352 ),
inference(forward_demodulation,[],[f3664,f2312]) ).
fof(f3664,plain,
( null_class = intersection(identity_relation,complement(subset_relation))
| ~ spl0_293
| ~ spl0_352 ),
inference(duplicate_literal_removal,[],[f3659]) ).
fof(f3659,plain,
( null_class = intersection(identity_relation,complement(subset_relation))
| null_class = intersection(identity_relation,complement(subset_relation))
| ~ spl0_293
| ~ spl0_352 ),
inference(resolution,[],[f3530,f2823]) ).
fof(f2823,plain,
( ! [X0] :
( member(regular(intersection(identity_relation,X0)),subset_relation)
| null_class = intersection(identity_relation,X0) )
| ~ spl0_293 ),
inference(avatar_component_clause,[],[f2822]) ).
fof(f9396,plain,
( spl0_624
| ~ spl0_235
| ~ spl0_619 ),
inference(avatar_split_clause,[],[f9368,f9365,f2310,f9394]) ).
fof(f9394,plain,
( spl0_624
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation)
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),X1)
| subclass(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f9365,plain,
( spl0_619
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),X1)
| subclass(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f9368,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation)
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),X1)
| subclass(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))) )
| ~ spl0_235
| ~ spl0_619 ),
inference(forward_demodulation,[],[f9366,f2312]) ).
fof(f9366,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),X1)
| subclass(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) )
| ~ spl0_619 ),
inference(avatar_component_clause,[],[f9365]) ).
fof(f9392,plain,
( spl0_623
| ~ spl0_235
| ~ spl0_618 ),
inference(avatar_split_clause,[],[f9363,f9358,f2310,f9390]) ).
fof(f9390,plain,
( spl0_623
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),singleton_relation)
| subclass(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation)))))
| ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f9358,plain,
( spl0_618
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),X1)
| subclass(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation)))))
| ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f9363,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),singleton_relation)
| subclass(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation)))))
| ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),X1) )
| ~ spl0_235
| ~ spl0_618 ),
inference(forward_demodulation,[],[f9362,f2312]) ).
fof(f9362,plain,
( ! [X0,X1] :
( subclass(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation)))))
| ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),X1)
| ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) )
| ~ spl0_235
| ~ spl0_618 ),
inference(forward_demodulation,[],[f9361,f2312]) ).
fof(f9361,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),X1)
| subclass(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation)))))
| ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) )
| ~ spl0_235
| ~ spl0_618 ),
inference(forward_demodulation,[],[f9359,f2312]) ).
fof(f9359,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),X1)
| subclass(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation)))))
| ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) )
| ~ spl0_618 ),
inference(avatar_component_clause,[],[f9358]) ).
fof(f9380,plain,
( spl0_621
| ~ spl0_622
| ~ spl0_61
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1878,f1868,f524,f9377,f9374]) ).
fof(f9374,plain,
( spl0_621
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f9377,plain,
( spl0_622
<=> subclass(composition_function,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f524,plain,
( spl0_61
<=> ! [X0,X1] :
( member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f1878,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,element_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))) )
| ~ spl0_61
| ~ spl0_205 ),
inference(resolution,[],[f1869,f525]) ).
fof(f525,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| member(X0,X1) )
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f524]) ).
fof(f9372,plain,
( spl0_620
| ~ spl0_38
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1623,f1620,f372,f9370]) ).
fof(f9370,plain,
( spl0_620
<=> ! [X2,X0,X1] :
( null_class = X0
| ~ subclass(X0,X1)
| ~ member(X0,universal_class)
| ~ subclass(X1,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f1623,plain,
( ! [X2,X0,X1] :
( null_class = X0
| ~ subclass(X0,X1)
| ~ member(X0,universal_class)
| ~ subclass(X1,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) )
| ~ spl0_38
| ~ spl0_193 ),
inference(resolution,[],[f1621,f373]) ).
fof(f9367,plain,
( spl0_619
| ~ spl0_125
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1396,f1365,f959,f9365]) ).
fof(f1396,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),X1)
| subclass(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) )
| ~ spl0_125
| ~ spl0_164 ),
inference(resolution,[],[f1366,f960]) ).
fof(f9360,plain,
( spl0_618
| ~ spl0_124
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1394,f1365,f955,f9358]) ).
fof(f1394,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),X1)
| subclass(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation)))))
| ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) )
| ~ spl0_124
| ~ spl0_164 ),
inference(resolution,[],[f1366,f956]) ).
fof(f9355,plain,
( spl0_617
| ~ spl0_135
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1214,f1167,f1087,f9353]) ).
fof(f9353,plain,
( spl0_617
<=> ! [X0,X1] :
( ~ member(not_subclass_element(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1),subset_relation)
| member(not_subclass_element(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1),identity_relation)
| subclass(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f1214,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1),subset_relation)
| member(not_subclass_element(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1),identity_relation)
| subclass(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1) )
| ~ spl0_135
| ~ spl0_144 ),
inference(resolution,[],[f1168,f1088]) ).
fof(f9351,plain,
( spl0_616
| ~ spl0_128
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f3668,f3529,f1004,f9349]) ).
fof(f3668,plain,
( ! [X0] : null_class = intersection(X0,complement(X0))
| ~ spl0_128
| ~ spl0_352 ),
inference(duplicate_literal_removal,[],[f3647]) ).
fof(f3647,plain,
( ! [X0] :
( null_class = intersection(X0,complement(X0))
| null_class = intersection(X0,complement(X0)) )
| ~ spl0_128
| ~ spl0_352 ),
inference(resolution,[],[f3530,f1005]) ).
fof(f9346,plain,
( spl0_615
| ~ spl0_134
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1207,f1167,f1083,f9344]) ).
fof(f9344,plain,
( spl0_615
<=> ! [X0,X1] :
( ~ member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),subset_relation)
| member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),identity_relation)
| subclass(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f1207,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),subset_relation)
| member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),identity_relation)
| subclass(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1) )
| ~ spl0_134
| ~ spl0_144 ),
inference(resolution,[],[f1168,f1084]) ).
fof(f9339,plain,
( spl0_614
| ~ spl0_135
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1200,f1163,f1087,f9337]) ).
fof(f9337,plain,
( spl0_614
<=> ! [X0,X1] :
( ~ member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),element_relation)
| member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),singleton_relation)
| subclass(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f1200,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),element_relation)
| member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),singleton_relation)
| subclass(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1) )
| ~ spl0_135
| ~ spl0_143 ),
inference(resolution,[],[f1164,f1088]) ).
fof(f9332,plain,
( spl0_613
| ~ spl0_134
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1193,f1163,f1083,f9330]) ).
fof(f9330,plain,
( spl0_613
<=> ! [X0,X1] :
( ~ member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),element_relation)
| member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),singleton_relation)
| subclass(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f1193,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),element_relation)
| member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),singleton_relation)
| subclass(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1) )
| ~ spl0_134
| ~ spl0_143 ),
inference(resolution,[],[f1164,f1084]) ).
fof(f9328,plain,
( spl0_612
| ~ spl0_88
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f882,f823,f677,f9326]) ).
fof(f9326,plain,
( spl0_612
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),subset_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f677,plain,
( spl0_88
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f882,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),subset_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1)) )
| ~ spl0_88
| ~ spl0_111 ),
inference(resolution,[],[f824,f678]) ).
fof(f678,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0)) )
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f9235,plain,
( spl0_611
| ~ spl0_294
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f3666,f3529,f2826,f9232]) ).
fof(f9232,plain,
( spl0_611
<=> null_class = intersection(singleton_relation,complement(element_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f2826,plain,
( spl0_294
<=> ! [X0] :
( null_class = intersection(singleton_relation,X0)
| member(regular(intersection(singleton_relation,X0)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f3666,plain,
( null_class = intersection(singleton_relation,complement(element_relation))
| ~ spl0_294
| ~ spl0_352 ),
inference(duplicate_literal_removal,[],[f3650]) ).
fof(f3650,plain,
( null_class = intersection(singleton_relation,complement(element_relation))
| null_class = intersection(singleton_relation,complement(element_relation))
| ~ spl0_294
| ~ spl0_352 ),
inference(resolution,[],[f3530,f2827]) ).
fof(f2827,plain,
( ! [X0] :
( member(regular(intersection(singleton_relation,X0)),element_relation)
| null_class = intersection(singleton_relation,X0) )
| ~ spl0_294 ),
inference(avatar_component_clause,[],[f2826]) ).
fof(f9208,plain,
( spl0_610
| ~ spl0_86
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1722,f1711,f669,f9206]) ).
fof(f9206,plain,
( spl0_610
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
| member(first(regular(cross_product(X0,X1))),domain_of(X2))
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f669,plain,
( spl0_86
<=> ! [X4,X0,X1] :
( member(X1,domain_of(X0))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f1722,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
| member(first(regular(cross_product(X0,X1))),domain_of(X2))
| cross_product(X0,X1) = null_class )
| ~ spl0_86
| ~ spl0_198 ),
inference(superposition,[],[f670,f1712]) ).
fof(f670,plain,
( ! [X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function)
| member(X1,domain_of(X0)) )
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f669]) ).
fof(f9204,plain,
( spl0_609
| ~ spl0_85
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1721,f1711,f664,f9202]) ).
fof(f9202,plain,
( spl0_609
<=> ! [X0,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| member(regular(cross_product(X0,X1)),element_relation)
| ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f1721,plain,
( ! [X0,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| member(regular(cross_product(X0,X1)),element_relation)
| ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = null_class )
| ~ spl0_85
| ~ spl0_198 ),
inference(superposition,[],[f665,f1712]) ).
fof(f9200,plain,
( spl0_608
| ~ spl0_31
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1627,f1620,f335,f9198]) ).
fof(f9198,plain,
( spl0_608
<=> ! [X2,X0,X1] :
( null_class = X0
| ~ subclass(X0,intersection(X1,X2))
| ~ member(X0,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f1627,plain,
( ! [X2,X0,X1] :
( null_class = X0
| ~ subclass(X0,intersection(X1,X2))
| ~ member(X0,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
| ~ spl0_31
| ~ spl0_193 ),
inference(resolution,[],[f1621,f336]) ).
fof(f9196,plain,
( spl0_607
| ~ spl0_32
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1626,f1620,f339,f9194]) ).
fof(f9194,plain,
( spl0_607
<=> ! [X2,X0,X1] :
( null_class = X0
| ~ subclass(X0,intersection(X1,X2))
| ~ member(X0,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f1626,plain,
( ! [X2,X0,X1] :
( null_class = X0
| ~ subclass(X0,intersection(X1,X2))
| ~ member(X0,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) )
| ~ spl0_32
| ~ spl0_193 ),
inference(resolution,[],[f1621,f340]) ).
fof(f9192,plain,
( spl0_606
| ~ spl0_130
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1574,f1556,f1012,f9190]) ).
fof(f9190,plain,
( spl0_606
<=> ! [X0,X1] :
( member(not_subclass_element(X0,X1),subset_relation)
| ~ member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class))
| ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f1574,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,X1),subset_relation)
| ~ member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class))
| ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subclass(X0,X1) )
| ~ spl0_130
| ~ spl0_185 ),
inference(resolution,[],[f1557,f1013]) ).
fof(f9188,plain,
( spl0_605
| ~ spl0_44
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1393,f1365,f424,f9186]) ).
fof(f9186,plain,
( spl0_605
<=> ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,complement(X2))),X1)
| subclass(X0,intersection(X1,complement(X2)))
| member(not_subclass_element(X0,intersection(X1,complement(X2))),X2)
| ~ member(not_subclass_element(X0,intersection(X1,complement(X2))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f1393,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,complement(X2))),X1)
| subclass(X0,intersection(X1,complement(X2)))
| member(not_subclass_element(X0,intersection(X1,complement(X2))),X2)
| ~ member(not_subclass_element(X0,intersection(X1,complement(X2))),universal_class) )
| ~ spl0_44
| ~ spl0_164 ),
inference(resolution,[],[f1366,f425]) ).
fof(f9184,plain,
( spl0_604
| ~ spl0_79
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f974,f919,f628,f9182]) ).
fof(f9182,plain,
( spl0_604
<=> ! [X2,X0,X1] :
( ~ subclass(X0,cross_product(X1,X2))
| null_class = X0
| regular(X0) = unordered_pair(unordered_pair(first(regular(X0)),first(regular(X0))),unordered_pair(first(regular(X0)),unordered_pair(second(regular(X0)),second(regular(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f974,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,cross_product(X1,X2))
| null_class = X0
| regular(X0) = unordered_pair(unordered_pair(first(regular(X0)),first(regular(X0))),unordered_pair(first(regular(X0)),unordered_pair(second(regular(X0)),second(regular(X0))))) )
| ~ spl0_79
| ~ spl0_116 ),
inference(resolution,[],[f920,f629]) ).
fof(f9141,plain,
( spl0_603
| ~ spl0_129
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f3640,f3525,f1008,f9139]) ).
fof(f3640,plain,
( ! [X0] : null_class = intersection(complement(X0),X0)
| ~ spl0_129
| ~ spl0_351 ),
inference(duplicate_literal_removal,[],[f3617]) ).
fof(f3617,plain,
( ! [X0] :
( null_class = intersection(complement(X0),X0)
| null_class = intersection(complement(X0),X0) )
| ~ spl0_129
| ~ spl0_351 ),
inference(resolution,[],[f3526,f1009]) ).
fof(f9131,plain,
( ~ spl0_602
| ~ spl0_235
| spl0_601 ),
inference(avatar_split_clause,[],[f9126,f9122,f2310,f9128]) ).
fof(f9128,plain,
( spl0_602
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f9122,plain,
( spl0_601
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f9126,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_235
| spl0_601 ),
inference(forward_demodulation,[],[f9123,f2312]) ).
fof(f9123,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class))))
| spl0_601 ),
inference(avatar_component_clause,[],[f9122]) ).
fof(f9125,plain,
( ~ spl0_548
| spl0_233
| spl0_601
| ~ spl0_43
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1702,f1660,f393,f9122,f2300,f8195]) ).
fof(f8195,plain,
( spl0_548
<=> member(identity_relation,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f2300,plain,
( spl0_233
<=> null_class = identity_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f1702,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class))))
| null_class = identity_relation
| ~ member(identity_relation,universal_class)
| ~ spl0_43
| ~ spl0_196 ),
inference(superposition,[],[f1661,f395]) ).
fof(f9120,plain,
( spl0_600
| ~ spl0_20
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1629,f1620,f287,f9118]) ).
fof(f9118,plain,
( spl0_600
<=> ! [X0,X1] :
( null_class = X0
| ~ subclass(X0,complement(X1))
| ~ member(X0,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f1629,plain,
( ! [X0,X1] :
( null_class = X0
| ~ subclass(X0,complement(X1))
| ~ member(X0,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
| ~ spl0_20
| ~ spl0_193 ),
inference(resolution,[],[f1621,f288]) ).
fof(f9115,plain,
( spl0_599
| ~ spl0_129
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1213,f1167,f1008,f9113]) ).
fof(f9113,plain,
( spl0_599
<=> ! [X0] :
( ~ member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),subset_relation)
| member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
| null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f1213,plain,
( ! [X0] :
( ~ member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),subset_relation)
| member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
| null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_129
| ~ spl0_144 ),
inference(resolution,[],[f1168,f1009]) ).
fof(f9110,plain,
( spl0_598
| ~ spl0_128
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1211,f1167,f1004,f9108]) ).
fof(f9108,plain,
( spl0_598
<=> ! [X0] :
( ~ member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),subset_relation)
| member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),identity_relation)
| null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f1211,plain,
( ! [X0] :
( ~ member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),subset_relation)
| member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),identity_relation)
| null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) )
| ~ spl0_128
| ~ spl0_144 ),
inference(resolution,[],[f1168,f1005]) ).
fof(f9103,plain,
( spl0_597
| ~ spl0_129
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1199,f1163,f1008,f9101]) ).
fof(f9101,plain,
( spl0_597
<=> ! [X0] :
( ~ member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),element_relation)
| member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
| null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f1199,plain,
( ! [X0] :
( ~ member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),element_relation)
| member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
| null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_129
| ~ spl0_143 ),
inference(resolution,[],[f1164,f1009]) ).
fof(f9096,plain,
( spl0_596
| ~ spl0_128
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1197,f1163,f1004,f9094]) ).
fof(f9094,plain,
( spl0_596
<=> ! [X0] :
( ~ member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),element_relation)
| member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),singleton_relation)
| null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f1197,plain,
( ! [X0] :
( ~ member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),element_relation)
| member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),singleton_relation)
| null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0) )
| ~ spl0_128
| ~ spl0_143 ),
inference(resolution,[],[f1164,f1005]) ).
fof(f9092,plain,
( spl0_595
| ~ spl0_50
| ~ spl0_70
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f970,f915,f568,f452,f9090]) ).
fof(f9090,plain,
( spl0_595
<=> ! [X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(complement(domain_of(X0)),X1),not_subclass_element(complement(domain_of(X0)),X1)),universal_class))
| subclass(complement(domain_of(X0)),X1)
| ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f970,plain,
( ! [X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(complement(domain_of(X0)),X1),not_subclass_element(complement(domain_of(X0)),X1)),universal_class))
| subclass(complement(domain_of(X0)),X1)
| ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class) )
| ~ spl0_50
| ~ spl0_70
| ~ spl0_115 ),
inference(forward_demodulation,[],[f969,f453]) ).
fof(f969,plain,
( ! [X0,X1] :
( subclass(complement(domain_of(X0)),X1)
| ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class)
| null_class = intersection(cross_product(unordered_pair(not_subclass_element(complement(domain_of(X0)),X1),not_subclass_element(complement(domain_of(X0)),X1)),universal_class),X0) )
| ~ spl0_70
| ~ spl0_115 ),
inference(resolution,[],[f916,f569]) ).
fof(f9078,plain,
( spl0_594
| ~ spl0_300
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f3638,f3525,f2930,f9075]) ).
fof(f9075,plain,
( spl0_594
<=> null_class = intersection(complement(element_relation),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f2930,plain,
( spl0_300
<=> ! [X0] :
( null_class = intersection(X0,singleton_relation)
| member(regular(intersection(X0,singleton_relation)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f3638,plain,
( null_class = intersection(complement(element_relation),singleton_relation)
| ~ spl0_300
| ~ spl0_351 ),
inference(duplicate_literal_removal,[],[f3620]) ).
fof(f3620,plain,
( null_class = intersection(complement(element_relation),singleton_relation)
| null_class = intersection(complement(element_relation),singleton_relation)
| ~ spl0_300
| ~ spl0_351 ),
inference(resolution,[],[f3526,f2931]) ).
fof(f2931,plain,
( ! [X0] :
( member(regular(intersection(X0,singleton_relation)),element_relation)
| null_class = intersection(X0,singleton_relation) )
| ~ spl0_300 ),
inference(avatar_component_clause,[],[f2930]) ).
fof(f9064,plain,
( spl0_593
| ~ spl0_235
| ~ spl0_590 ),
inference(avatar_split_clause,[],[f8995,f8992,f2310,f9062]) ).
fof(f9062,plain,
( spl0_593
<=> ! [X0] :
( ~ subclass(X0,singleton_relation)
| null_class = X0
| ~ member(X0,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f8992,plain,
( spl0_590
<=> ! [X0] :
( null_class = X0
| ~ subclass(X0,identity_relation)
| ~ member(X0,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f8995,plain,
( ! [X0] :
( ~ subclass(X0,singleton_relation)
| null_class = X0
| ~ member(X0,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_235
| ~ spl0_590 ),
inference(forward_demodulation,[],[f8993,f2312]) ).
fof(f8993,plain,
( ! [X0] :
( null_class = X0
| ~ subclass(X0,identity_relation)
| ~ member(X0,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_590 ),
inference(avatar_component_clause,[],[f8992]) ).
fof(f9003,plain,
( spl0_592
| ~ spl0_72
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1755,f1745,f584,f9001]) ).
fof(f9001,plain,
( spl0_592
<=> ! [X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),compose_class(X3))
| ~ operation(X2)
| not_homomorphism2(X0,X1,X2) = compose(X3,not_homomorphism1(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f1755,plain,
( ! [X2,X3,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),compose_class(X3))
| ~ operation(X2)
| not_homomorphism2(X0,X1,X2) = compose(X3,not_homomorphism1(X0,X1,X2)) )
| ~ spl0_72
| ~ spl0_199 ),
inference(resolution,[],[f1746,f585]) ).
fof(f8999,plain,
( spl0_591
| ~ spl0_97
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1637,f1620,f731,f8997]) ).
fof(f8997,plain,
( spl0_591
<=> ! [X0] :
( null_class = X0
| ~ subclass(X0,singleton_relation)
| ~ member(X0,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f1637,plain,
( ! [X0] :
( null_class = X0
| ~ subclass(X0,singleton_relation)
| ~ member(X0,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation) )
| ~ spl0_97
| ~ spl0_193 ),
inference(resolution,[],[f1621,f732]) ).
fof(f8994,plain,
( spl0_590
| ~ spl0_103
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1635,f1620,f761,f8992]) ).
fof(f1635,plain,
( ! [X0] :
( null_class = X0
| ~ subclass(X0,identity_relation)
| ~ member(X0,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_103
| ~ spl0_193 ),
inference(resolution,[],[f1621,f762]) ).
fof(f8990,plain,
( spl0_589
| ~ spl0_116
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1571,f1556,f919,f8988]) ).
fof(f8988,plain,
( spl0_589
<=> ! [X0] :
( member(regular(X0),subset_relation)
| ~ member(regular(X0),cross_product(universal_class,universal_class))
| ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f1571,plain,
( ! [X0] :
( member(regular(X0),subset_relation)
| ~ member(regular(X0),cross_product(universal_class,universal_class))
| ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| null_class = X0 )
| ~ spl0_116
| ~ spl0_185 ),
inference(resolution,[],[f1557,f920]) ).
fof(f8986,plain,
( spl0_588
| ~ spl0_89
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f832,f802,f682,f8984]) ).
fof(f8984,plain,
( spl0_588
<=> ! [X2,X0,X1,X3] :
( ~ subclass(universal_class,compose(X0,X1))
| member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f832,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,compose(X0,X1))
| member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) )
| ~ spl0_89
| ~ spl0_106 ),
inference(resolution,[],[f803,f683]) ).
fof(f8982,plain,
( spl0_587
| ~ spl0_312
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f3636,f3525,f3118,f8979]) ).
fof(f8979,plain,
( spl0_587
<=> null_class = intersection(complement(subset_relation),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f3118,plain,
( spl0_312
<=> ! [X0] :
( member(regular(intersection(X0,singleton_relation)),subset_relation)
| null_class = intersection(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f3636,plain,
( null_class = intersection(complement(subset_relation),singleton_relation)
| ~ spl0_312
| ~ spl0_351 ),
inference(duplicate_literal_removal,[],[f3629]) ).
fof(f3629,plain,
( null_class = intersection(complement(subset_relation),singleton_relation)
| null_class = intersection(complement(subset_relation),singleton_relation)
| ~ spl0_312
| ~ spl0_351 ),
inference(resolution,[],[f3526,f3119]) ).
fof(f3119,plain,
( ! [X0] :
( member(regular(intersection(X0,singleton_relation)),subset_relation)
| null_class = intersection(X0,singleton_relation) )
| ~ spl0_312 ),
inference(avatar_component_clause,[],[f3118]) ).
fof(f8855,plain,
( spl0_586
| ~ spl0_77
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1719,f1711,f613,f8853]) ).
fof(f8853,plain,
( spl0_586
<=> ! [X0,X3,X2,X1] :
( member(regular(cross_product(X0,X1)),cross_product(X2,X3))
| ~ member(second(regular(cross_product(X0,X1))),X3)
| ~ member(first(regular(cross_product(X0,X1))),X2)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f1719,plain,
( ! [X2,X3,X0,X1] :
( member(regular(cross_product(X0,X1)),cross_product(X2,X3))
| ~ member(second(regular(cross_product(X0,X1))),X3)
| ~ member(first(regular(cross_product(X0,X1))),X2)
| cross_product(X0,X1) = null_class )
| ~ spl0_77
| ~ spl0_198 ),
inference(superposition,[],[f614,f1712]) ).
fof(f8848,plain,
( ~ spl0_584
| spl0_274
| spl0_585
| ~ spl0_76
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1700,f1660,f608,f8845,f2535,f8841]) ).
fof(f8841,plain,
( spl0_584
<=> member(subset_relation,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f8845,plain,
( spl0_585
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f608,plain,
( spl0_76
<=> subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1700,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| null_class = subset_relation
| ~ member(subset_relation,universal_class)
| ~ spl0_76
| ~ spl0_196 ),
inference(superposition,[],[f1661,f610]) ).
fof(f610,plain,
( subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f608]) ).
fof(f8839,plain,
( spl0_583
| ~ spl0_152
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f1643,f1639,f1247,f8837]) ).
fof(f8837,plain,
( spl0_583
<=> ! [X0] :
( complement(X0) = null_class
| ~ member(complement(X0),universal_class)
| ~ subclass(universal_class,X0)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f1643,plain,
( ! [X0] :
( complement(X0) = null_class
| ~ member(complement(X0),universal_class)
| ~ subclass(universal_class,X0)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class)))),universal_class) )
| ~ spl0_152
| ~ spl0_194 ),
inference(resolution,[],[f1640,f1248]) ).
fof(f8835,plain,
( spl0_582
| ~ spl0_28
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f3129,f3092,f323,f8833]) ).
fof(f8833,plain,
( spl0_582
<=> ! [X0] :
( subclass(X0,subset_relation)
| ~ subclass(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f3129,plain,
( ! [X0] :
( subclass(X0,subset_relation)
| ~ subclass(X0,singleton_relation) )
| ~ spl0_28
| ~ spl0_310 ),
inference(duplicate_literal_removal,[],[f3121]) ).
fof(f3121,plain,
( ! [X0] :
( subclass(X0,subset_relation)
| ~ subclass(X0,singleton_relation)
| subclass(X0,subset_relation) )
| ~ spl0_28
| ~ spl0_310 ),
inference(resolution,[],[f3093,f324]) ).
fof(f8831,plain,
( spl0_581
| ~ spl0_38
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1582,f1578,f372,f8829]) ).
fof(f8829,plain,
( spl0_581
<=> ! [X2,X0,X1] :
( ~ member(compose(X0,X1),universal_class)
| ~ member(X1,universal_class)
| ~ subclass(compose_class(X0),X2)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f1582,plain,
( ! [X2,X0,X1] :
( ~ member(compose(X0,X1),universal_class)
| ~ member(X1,universal_class)
| ~ subclass(compose_class(X0),X2)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),X2) )
| ~ spl0_38
| ~ spl0_186 ),
inference(resolution,[],[f1579,f373]) ).
fof(f8827,plain,
( ~ spl0_579
| spl0_580
| ~ spl0_106
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1573,f1556,f802,f8825,f8821]) ).
fof(f8821,plain,
( spl0_579
<=> subclass(universal_class,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f8825,plain,
( spl0_580
<=> ! [X0,X1] :
( member(unordered_pair(X0,X1),subset_relation)
| ~ member(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f1573,plain,
( ! [X0,X1] :
( member(unordered_pair(X0,X1),subset_relation)
| ~ member(unordered_pair(X0,X1),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
| ~ spl0_106
| ~ spl0_185 ),
inference(resolution,[],[f1557,f803]) ).
fof(f8819,plain,
( spl0_578
| ~ spl0_76
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1401,f1365,f608,f8817]) ).
fof(f8817,plain,
( spl0_578
<=> ! [X0] :
( ~ member(not_subclass_element(X0,subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(not_subclass_element(X0,subset_relation),cross_product(universal_class,universal_class))
| subclass(X0,subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f1401,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(not_subclass_element(X0,subset_relation),cross_product(universal_class,universal_class))
| subclass(X0,subset_relation) )
| ~ spl0_76
| ~ spl0_164 ),
inference(superposition,[],[f1366,f610]) ).
fof(f8815,plain,
( spl0_577
| ~ spl0_130
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1314,f1294,f1012,f8813]) ).
fof(f8813,plain,
( spl0_577
<=> ! [X0,X1] :
( null_class = cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class)
| ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class))))
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f1314,plain,
( ! [X0,X1] :
( null_class = cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class)
| ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class))))
| subclass(X0,X1) )
| ~ spl0_130
| ~ spl0_158 ),
inference(resolution,[],[f1295,f1013]) ).
fof(f8728,plain,
( spl0_576
| ~ spl0_28
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3103,f2940,f323,f8726]) ).
fof(f8726,plain,
( spl0_576
<=> ! [X0] :
( subclass(X0,element_relation)
| ~ subclass(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f3103,plain,
( ! [X0] :
( subclass(X0,element_relation)
| ~ subclass(X0,singleton_relation) )
| ~ spl0_28
| ~ spl0_302 ),
inference(duplicate_literal_removal,[],[f3095]) ).
fof(f3095,plain,
( ! [X0] :
( subclass(X0,element_relation)
| ~ subclass(X0,singleton_relation)
| subclass(X0,element_relation) )
| ~ spl0_28
| ~ spl0_302 ),
inference(resolution,[],[f2941,f324]) ).
fof(f8724,plain,
( spl0_575
| ~ spl0_64
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1756,f1745,f539,f8722]) ).
fof(f8722,plain,
( spl0_575
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_relation)
| ~ operation(X2)
| not_homomorphism2(X0,X1,X2) = domain_of(not_homomorphism1(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f1756,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_relation)
| ~ operation(X2)
| not_homomorphism2(X0,X1,X2) = domain_of(not_homomorphism1(X0,X1,X2)) )
| ~ spl0_64
| ~ spl0_199 ),
inference(resolution,[],[f1746,f540]) ).
fof(f8720,plain,
( spl0_574
| ~ spl0_114
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1385,f1361,f892,f8718]) ).
fof(f8718,plain,
( spl0_574
<=> ! [X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) = X1
| not_subclass_element(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) = X0
| function(unordered_pair(X0,X1))
| ~ single_valued_class(unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f1385,plain,
( ! [X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) = X1
| not_subclass_element(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) = X0
| function(unordered_pair(X0,X1))
| ~ single_valued_class(unordered_pair(X0,X1)) )
| ~ spl0_114
| ~ spl0_163 ),
inference(resolution,[],[f1362,f893]) ).
fof(f8716,plain,
( spl0_573
| ~ spl0_142
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1270,f1247,f1159,f8714]) ).
fof(f8714,plain,
( spl0_573
<=> ! [X0,X1] :
( ~ subclass(universal_class,regular(X0))
| ~ member(X1,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),null_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f1270,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,regular(X0))
| ~ member(X1,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),null_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0)
| null_class = X0 )
| ~ spl0_142
| ~ spl0_152 ),
inference(resolution,[],[f1248,f1160]) ).
fof(f8712,plain,
( spl0_572
| ~ spl0_435
| ~ spl0_143
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1265,f1247,f1163,f5514,f8710]) ).
fof(f8710,plain,
( spl0_572
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),singleton_relation)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f1265,plain,
( ! [X0] :
( ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),singleton_relation) )
| ~ spl0_143
| ~ spl0_152 ),
inference(resolution,[],[f1248,f1164]) ).
fof(f8708,plain,
( spl0_571
| ~ spl0_76
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1256,f1243,f608,f8706]) ).
fof(f8706,plain,
( spl0_571
<=> ! [X0,X1] :
( ~ subclass(subset_relation,X0)
| ~ member(X1,cross_product(universal_class,universal_class))
| ~ member(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f1243,plain,
( spl0_151
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| ~ subclass(intersection(X2,X1),X3)
| member(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f1256,plain,
( ! [X0,X1] :
( ~ subclass(subset_relation,X0)
| ~ member(X1,cross_product(universal_class,universal_class))
| ~ member(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| member(X1,X0) )
| ~ spl0_76
| ~ spl0_151 ),
inference(superposition,[],[f1244,f610]) ).
fof(f1244,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(intersection(X2,X1),X3)
| ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,X3) )
| ~ spl0_151 ),
inference(avatar_component_clause,[],[f1243]) ).
fof(f8704,plain,
( spl0_570
| ~ spl0_50
| ~ spl0_70
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f899,f884,f568,f452,f8702]) ).
fof(f8702,plain,
( spl0_570
<=> ! [X0] :
( null_class = intersection(X0,cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class))
| null_class = complement(domain_of(X0))
| ~ member(regular(complement(domain_of(X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f899,plain,
( ! [X0] :
( null_class = intersection(X0,cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class))
| null_class = complement(domain_of(X0))
| ~ member(regular(complement(domain_of(X0))),universal_class) )
| ~ spl0_50
| ~ spl0_70
| ~ spl0_112 ),
inference(forward_demodulation,[],[f898,f453]) ).
fof(f898,plain,
( ! [X0] :
( null_class = complement(domain_of(X0))
| ~ member(regular(complement(domain_of(X0))),universal_class)
| null_class = intersection(cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class),X0) )
| ~ spl0_70
| ~ spl0_112 ),
inference(resolution,[],[f885,f569]) ).
fof(f8669,plain,
( spl0_569
| ~ spl0_4
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f2961,f2814,f219,f8667]) ).
fof(f2814,plain,
( spl0_291
<=> ! [X0,X1] :
( ~ member(X0,subset_relation)
| ~ subclass(cross_product(universal_class,universal_class),X1)
| member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f2961,plain,
( ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,universal_class) )
| ~ spl0_4
| ~ spl0_291 ),
inference(resolution,[],[f2815,f220]) ).
fof(f2815,plain,
( ! [X0,X1] :
( ~ subclass(cross_product(universal_class,universal_class),X1)
| ~ member(X0,subset_relation)
| member(X0,X1) )
| ~ spl0_291 ),
inference(avatar_component_clause,[],[f2814]) ).
fof(f8357,plain,
( spl0_568
| ~ spl0_61
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1751,f1745,f524,f8355]) ).
fof(f8355,plain,
( spl0_568
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),element_relation)
| ~ operation(X2)
| member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f1751,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),element_relation)
| ~ operation(X2)
| member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) )
| ~ spl0_61
| ~ spl0_199 ),
inference(resolution,[],[f1746,f525]) ).
fof(f8353,plain,
( spl0_567
| ~ spl0_72
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1718,f1711,f584,f8351]) ).
fof(f8351,plain,
( spl0_567
<=> ! [X2,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),compose_class(X2))
| second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f1718,plain,
( ! [X2,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),compose_class(X2))
| second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = null_class )
| ~ spl0_72
| ~ spl0_198 ),
inference(superposition,[],[f585,f1712]) ).
fof(f8349,plain,
( spl0_566
| ~ spl0_103
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2870,f2310,f761,f8347]) ).
fof(f8347,plain,
( spl0_566
<=> ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f2870,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,subset_relation) )
| ~ spl0_103
| ~ spl0_235 ),
inference(superposition,[],[f762,f2312]) ).
fof(f8345,plain,
( spl0_565
| ~ spl0_134
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1606,f1584,f1083,f8343]) ).
fof(f8343,plain,
( spl0_565
<=> ! [X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X1),domain_of(X0)),not_subclass_element(intersection(universal_class,X1),domain_of(X0))),universal_class))
| subclass(intersection(universal_class,X1),domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f1584,plain,
( spl0_187
<=> ! [X0,X1] :
( null_class = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
| ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
| subclass(X0,domain_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f1606,plain,
( ! [X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X1),domain_of(X0)),not_subclass_element(intersection(universal_class,X1),domain_of(X0))),universal_class))
| subclass(intersection(universal_class,X1),domain_of(X0)) )
| ~ spl0_134
| ~ spl0_187 ),
inference(duplicate_literal_removal,[],[f1601]) ).
fof(f1601,plain,
( ! [X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X1),domain_of(X0)),not_subclass_element(intersection(universal_class,X1),domain_of(X0))),universal_class))
| subclass(intersection(universal_class,X1),domain_of(X0))
| subclass(intersection(universal_class,X1),domain_of(X0)) )
| ~ spl0_134
| ~ spl0_187 ),
inference(resolution,[],[f1585,f1084]) ).
fof(f1585,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
| null_class = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
| subclass(X0,domain_of(X1)) )
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f1584]) ).
fof(f8341,plain,
( spl0_564
| ~ spl0_135
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1605,f1584,f1087,f8339]) ).
fof(f8339,plain,
( spl0_564
<=> ! [X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(X1,universal_class),domain_of(X0)),not_subclass_element(intersection(X1,universal_class),domain_of(X0))),universal_class))
| subclass(intersection(X1,universal_class),domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f1605,plain,
( ! [X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(X1,universal_class),domain_of(X0)),not_subclass_element(intersection(X1,universal_class),domain_of(X0))),universal_class))
| subclass(intersection(X1,universal_class),domain_of(X0)) )
| ~ spl0_135
| ~ spl0_187 ),
inference(duplicate_literal_removal,[],[f1602]) ).
fof(f1602,plain,
( ! [X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(X1,universal_class),domain_of(X0)),not_subclass_element(intersection(X1,universal_class),domain_of(X0))),universal_class))
| subclass(intersection(X1,universal_class),domain_of(X0))
| subclass(intersection(X1,universal_class),domain_of(X0)) )
| ~ spl0_135
| ~ spl0_187 ),
inference(resolution,[],[f1585,f1088]) ).
fof(f8337,plain,
( spl0_563
| ~ spl0_63
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1437,f1373,f532,f8335]) ).
fof(f8335,plain,
( spl0_563
<=> ! [X0,X1] :
( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class))))
| ~ member(X0,universal_class)
| member(X0,X1)
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f532,plain,
( spl0_63
<=> ! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1373,plain,
( spl0_166
<=> ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
| ~ subclass(domain_of(X1),X2)
| member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1437,plain,
( ! [X0,X1] :
( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class))))
| ~ member(X0,universal_class)
| member(X0,X1)
| ~ inductive(X1) )
| ~ spl0_63
| ~ spl0_166 ),
inference(resolution,[],[f1374,f533]) ).
fof(f533,plain,
( ! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) )
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f1374,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_of(X1),X2)
| null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
| ~ member(X0,universal_class)
| member(X0,X2) )
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1373]) ).
fof(f8323,plain,
( spl0_562
| ~ spl0_14
| ~ spl0_85
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1411,f1369,f664,f262,f8321]) ).
fof(f8321,plain,
( spl0_562
<=> ! [X0] :
( ~ member(X0,universal_class)
| ~ member(X0,domain_of(X0))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f1411,plain,
( ! [X0] :
( ~ subclass(domain_relation,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation)
| ~ member(X0,domain_of(X0)) )
| ~ spl0_85
| ~ spl0_165 ),
inference(resolution,[],[f1370,f665]) ).
fof(f8319,plain,
( spl0_561
| ~ spl0_123
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1397,f1365,f951,f8317]) ).
fof(f8317,plain,
( spl0_561
<=> ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),X1)
| subclass(X0,intersection(X1,regular(X2)))
| ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),null_class)
| null_class = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f1397,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),X1)
| subclass(X0,intersection(X1,regular(X2)))
| ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),null_class)
| null_class = X2 )
| ~ spl0_123
| ~ spl0_164 ),
inference(resolution,[],[f1366,f952]) ).
fof(f8315,plain,
( spl0_560
| ~ spl0_111
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1390,f1365,f823,f8313]) ).
fof(f8313,plain,
( spl0_560
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),X1)
| subclass(X0,intersection(X1,cross_product(universal_class,universal_class)))
| ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f1390,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),X1)
| subclass(X0,intersection(X1,cross_product(universal_class,universal_class)))
| ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),subset_relation) )
| ~ spl0_111
| ~ spl0_164 ),
inference(resolution,[],[f1366,f824]) ).
fof(f8310,plain,
( spl0_559
| ~ spl0_27
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1206,f1167,f319,f8308]) ).
fof(f8308,plain,
( spl0_559
<=> ! [X0] :
( ~ member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),subset_relation)
| member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),identity_relation)
| subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f1206,plain,
( ! [X0] :
( ~ member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),subset_relation)
| member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),identity_relation)
| subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0) )
| ~ spl0_27
| ~ spl0_144 ),
inference(resolution,[],[f1168,f320]) ).
fof(f8303,plain,
( spl0_558
| ~ spl0_27
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1192,f1163,f319,f8301]) ).
fof(f8301,plain,
( spl0_558
<=> ! [X0] :
( ~ member(not_subclass_element(complement(compose(element_relation,complement(identity_relation))),X0),element_relation)
| member(not_subclass_element(complement(compose(element_relation,complement(identity_relation))),X0),singleton_relation)
| subclass(complement(compose(element_relation,complement(identity_relation))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f1192,plain,
( ! [X0] :
( ~ member(not_subclass_element(complement(compose(element_relation,complement(identity_relation))),X0),element_relation)
| member(not_subclass_element(complement(compose(element_relation,complement(identity_relation))),X0),singleton_relation)
| subclass(complement(compose(element_relation,complement(identity_relation))),X0) )
| ~ spl0_27
| ~ spl0_143 ),
inference(resolution,[],[f1164,f320]) ).
fof(f8299,plain,
( spl0_557
| ~ spl0_135
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1186,f1159,f1087,f8297]) ).
fof(f8297,plain,
( spl0_557
<=> ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,regular(X1)),X2),null_class)
| ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
| null_class = X1
| subclass(intersection(X0,regular(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f1186,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,regular(X1)),X2),null_class)
| ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
| null_class = X1
| subclass(intersection(X0,regular(X1)),X2) )
| ~ spl0_135
| ~ spl0_142 ),
inference(resolution,[],[f1160,f1088]) ).
fof(f8236,plain,
( spl0_556
| ~ spl0_134
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1179,f1159,f1083,f8234]) ).
fof(f8234,plain,
( spl0_556
<=> ! [X2,X0,X1] :
( member(not_subclass_element(intersection(regular(X0),X1),X2),null_class)
| ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
| null_class = X0
| subclass(intersection(regular(X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f1179,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(regular(X0),X1),X2),null_class)
| ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
| null_class = X0
| subclass(intersection(regular(X0),X1),X2) )
| ~ spl0_134
| ~ spl0_142 ),
inference(resolution,[],[f1160,f1084]) ).
fof(f8232,plain,
( spl0_555
| ~ spl0_48
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1131,f1087,f444,f8230]) ).
fof(f8230,plain,
( spl0_555
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,unordered_pair(X1,X2)),X3)
| not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X1
| not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f1131,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,unordered_pair(X1,X2)),X3)
| not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X1
| not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X2 )
| ~ spl0_48
| ~ spl0_135 ),
inference(resolution,[],[f1088,f445]) ).
fof(f8228,plain,
( spl0_554
| ~ spl0_48
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1113,f1083,f444,f8226]) ).
fof(f8226,plain,
( spl0_554
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(unordered_pair(X0,X1),X2),X3)
| not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X0
| not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f1113,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(unordered_pair(X0,X1),X2),X3)
| not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X0
| not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X1 )
| ~ spl0_48
| ~ spl0_134 ),
inference(resolution,[],[f1084,f445]) ).
fof(f8224,plain,
( spl0_553
| ~ spl0_85
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f878,f823,f664,f8222]) ).
fof(f8222,plain,
( spl0_553
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f878,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1) )
| ~ spl0_85
| ~ spl0_111 ),
inference(resolution,[],[f824,f665]) ).
fof(f8220,plain,
( ~ spl0_2
| ~ spl0_551
| spl0_552
| ~ spl0_63
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f872,f819,f532,f8217,f8213,f209]) ).
fof(f209,plain,
( spl0_2
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f8213,plain,
( spl0_551
<=> inductive(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f8217,plain,
( spl0_552
<=> omega = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f872,plain,
( omega = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class))))
| ~ inductive(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class)))))
| ~ inductive(omega)
| ~ spl0_63
| ~ spl0_110 ),
inference(resolution,[],[f820,f533]) ).
fof(f8209,plain,
( ~ spl0_550
| ~ spl0_235
| spl0_549 ),
inference(avatar_split_clause,[],[f8203,f8199,f2310,f8206]) ).
fof(f8206,plain,
( spl0_550
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f8199,plain,
( spl0_549
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f8203,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),subset_relation)
| ~ spl0_235
| spl0_549 ),
inference(forward_demodulation,[],[f8200,f2312]) ).
fof(f8200,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation)
| spl0_549 ),
inference(avatar_component_clause,[],[f8199]) ).
fof(f8202,plain,
( spl0_233
| ~ spl0_548
| spl0_549
| ~ spl0_84
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f776,f761,f654,f8199,f8195,f2300]) ).
fof(f776,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation)
| ~ member(identity_relation,universal_class)
| null_class = identity_relation
| ~ spl0_84
| ~ spl0_103 ),
inference(resolution,[],[f762,f655]) ).
fof(f8193,plain,
( spl0_547
| ~ spl0_55
| ~ spl0_423 ),
inference(avatar_split_clause,[],[f7330,f5170,f477,f8190]) ).
fof(f8190,plain,
( spl0_547
<=> universal_class = intersection(universal_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f7330,plain,
( universal_class = intersection(universal_class,universal_class)
| ~ spl0_55
| ~ spl0_423 ),
inference(resolution,[],[f5171,f478]) ).
fof(f8186,plain,
( spl0_231
| ~ spl0_545
| spl0_546
| ~ spl0_84
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f772,f731,f654,f8183,f8179,f2282]) ).
fof(f8179,plain,
( spl0_545
<=> member(singleton_relation,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f8183,plain,
( spl0_546
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f772,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),element_relation)
| ~ member(singleton_relation,universal_class)
| null_class = singleton_relation
| ~ spl0_84
| ~ spl0_97 ),
inference(resolution,[],[f732,f655]) ).
fof(f8160,plain,
( spl0_544
| ~ spl0_67
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1749,f1745,f556,f8158]) ).
fof(f8158,plain,
( spl0_544
<=> ! [X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(X3,X4))
| ~ operation(X2)
| member(not_homomorphism2(X0,X1,X2),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f1749,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(X3,X4))
| ~ operation(X2)
| member(not_homomorphism2(X0,X1,X2),X4) )
| ~ spl0_67
| ~ spl0_199 ),
inference(resolution,[],[f1746,f557]) ).
fof(f8156,plain,
( spl0_543
| ~ spl0_68
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1748,f1745,f560,f8154]) ).
fof(f8154,plain,
( spl0_543
<=> ! [X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(X3,X4))
| ~ operation(X2)
| member(not_homomorphism1(X0,X1,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f560,plain,
( spl0_68
<=> ! [X0,X3,X2,X1] :
( member(X2,X0)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1748,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(X3,X4))
| ~ operation(X2)
| member(not_homomorphism1(X0,X1,X2),X3) )
| ~ spl0_68
| ~ spl0_199 ),
inference(resolution,[],[f1746,f561]) ).
fof(f561,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
| member(X2,X0) )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f8151,plain,
( spl0_542
| ~ spl0_228
| ~ spl0_423 ),
inference(avatar_split_clause,[],[f7329,f5170,f2265,f8148]) ).
fof(f8148,plain,
( spl0_542
<=> member(null_class,intersection(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f7329,plain,
( member(null_class,intersection(universal_class,universal_class))
| ~ spl0_228
| ~ spl0_423 ),
inference(resolution,[],[f5171,f2266]) ).
fof(f8146,plain,
( spl0_541
| ~ spl0_39
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1383,f1361,f376,f8144]) ).
fof(f8144,plain,
( spl0_541
<=> ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| ~ subclass(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f1383,plain,
( ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| ~ subclass(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = X2 )
| ~ spl0_39
| ~ spl0_163 ),
inference(resolution,[],[f1362,f377]) ).
fof(f8142,plain,
( spl0_540
| ~ spl0_106
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1313,f1294,f802,f8140]) ).
fof(f8140,plain,
( spl0_540
<=> ! [X0,X1] :
( null_class = cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)
| ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f1313,plain,
( ! [X0,X1] :
( null_class = cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)
| ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)))) )
| ~ spl0_106
| ~ spl0_158 ),
inference(resolution,[],[f1295,f803]) ).
fof(f8138,plain,
( spl0_539
| ~ spl0_48
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1260,f1247,f444,f8136]) ).
fof(f8136,plain,
( spl0_539
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| ~ member(X2,universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f1260,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| ~ member(X2,universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X1 )
| ~ spl0_48
| ~ spl0_152 ),
inference(resolution,[],[f1248,f445]) ).
fof(f7472,plain,
( spl0_538
| ~ spl0_64
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1715,f1711,f539,f7470]) ).
fof(f7470,plain,
( spl0_538
<=> ! [X0,X1] :
( ~ member(regular(cross_product(X0,X1)),domain_relation)
| second(regular(cross_product(X0,X1))) = domain_of(first(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f1715,plain,
( ! [X0,X1] :
( ~ member(regular(cross_product(X0,X1)),domain_relation)
| second(regular(cross_product(X0,X1))) = domain_of(first(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = null_class )
| ~ spl0_64
| ~ spl0_198 ),
inference(superposition,[],[f540,f1712]) ).
fof(f7468,plain,
( spl0_537
| ~ spl0_22
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1554,f1549,f295,f7466]) ).
fof(f7466,plain,
( spl0_537
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ function(cross_product(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f1554,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ function(cross_product(X1,X3)) )
| ~ spl0_22
| ~ spl0_184 ),
inference(resolution,[],[f1550,f296]) ).
fof(f7464,plain,
( spl0_536
| ~ spl0_38
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f1513,f1477,f372,f7462]) ).
fof(f7462,plain,
( spl0_536
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| ~ subclass(element_relation,X2)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f1513,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| ~ subclass(element_relation,X2)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2) )
| ~ spl0_38
| ~ spl0_176 ),
inference(resolution,[],[f1478,f373]) ).
fof(f7460,plain,
( spl0_535
| ~ spl0_38
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1498,f1456,f372,f7458]) ).
fof(f7458,plain,
( spl0_535
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f1498,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X2) )
| ~ spl0_38
| ~ spl0_171 ),
inference(resolution,[],[f1457,f373]) ).
fof(f7456,plain,
( spl0_534
| ~ spl0_38
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1480,f1452,f372,f7454]) ).
fof(f7454,plain,
( spl0_534
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ subclass(universal_class,X1)
| ~ member(X2,universal_class)
| ~ subclass(X1,X3)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f1480,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,X1)
| ~ member(X2,universal_class)
| ~ subclass(X1,X3)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X3) )
| ~ spl0_38
| ~ spl0_170 ),
inference(resolution,[],[f1453,f373]) ).
fof(f7446,plain,
( spl0_533
| ~ spl0_57
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1436,f1373,f503,f7444]) ).
fof(f7444,plain,
( spl0_533
<=> ! [X0,X1] :
( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(X1,universal_class))))
| ~ member(X0,universal_class)
| member(X0,domain_of(domain_of(X1)))
| ~ operation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f503,plain,
( spl0_57
<=> ! [X8] :
( ~ operation(X8)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f1436,plain,
( ! [X0,X1] :
( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(X1,universal_class))))
| ~ member(X0,universal_class)
| member(X0,domain_of(domain_of(X1)))
| ~ operation(X1) )
| ~ spl0_57
| ~ spl0_166 ),
inference(resolution,[],[f1374,f504]) ).
fof(f504,plain,
( ! [X8] :
( subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
| ~ operation(X8) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f7442,plain,
( spl0_532
| ~ spl0_110
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1384,f1361,f819,f7440]) ).
fof(f7440,plain,
( spl0_532
<=> ! [X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),omega) = X1
| not_subclass_element(unordered_pair(X0,X1),omega) = X0
| unordered_pair(X0,X1) = omega
| ~ inductive(unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f1384,plain,
( ! [X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),omega) = X1
| not_subclass_element(unordered_pair(X0,X1),omega) = X0
| unordered_pair(X0,X1) = omega
| ~ inductive(unordered_pair(X0,X1)) )
| ~ spl0_110
| ~ spl0_163 ),
inference(resolution,[],[f1362,f820]) ).
fof(f7438,plain,
( spl0_531
| ~ spl0_116
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1311,f1294,f919,f7436]) ).
fof(f7436,plain,
( spl0_531
<=> ! [X0] :
( null_class = cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)
| ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(regular(X0),regular(X0)),universal_class))))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f1311,plain,
( ! [X0] :
( null_class = cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)
| ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(regular(X0),regular(X0)),universal_class))))
| null_class = X0 )
| ~ spl0_116
| ~ spl0_158 ),
inference(resolution,[],[f1295,f920]) ).
fof(f7433,plain,
( ~ spl0_530
| ~ spl0_235
| spl0_528 ),
inference(avatar_split_clause,[],[f7425,f7417,f2310,f7430]) ).
fof(f7430,plain,
( spl0_530
<=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f7417,plain,
( spl0_528
<=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f7425,plain,
( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation)
| ~ spl0_235
| spl0_528 ),
inference(forward_demodulation,[],[f7418,f2312]) ).
fof(f7418,plain,
( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
| spl0_528 ),
inference(avatar_component_clause,[],[f7417]) ).
fof(f7424,plain,
( spl0_527
| spl0_528
| ~ spl0_529
| ~ spl0_23
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1210,f1167,f299,f7421,f7417,f7413]) ).
fof(f7421,plain,
( spl0_529
<=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f1210,plain,
( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation)
| member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
| null_class = domain_of(flip(cross_product(subset_relation,universal_class)))
| ~ spl0_23
| ~ spl0_144 ),
inference(resolution,[],[f1168,f300]) ).
fof(f7400,plain,
( ~ spl0_526
| ~ spl0_235
| spl0_522 ),
inference(avatar_split_clause,[],[f7384,f7375,f2310,f7397]) ).
fof(f7397,plain,
( spl0_526
<=> member(regular(complement(compose(element_relation,complement(singleton_relation)))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f7375,plain,
( spl0_522
<=> member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f7384,plain,
( ~ member(regular(complement(compose(element_relation,complement(singleton_relation)))),singleton_relation)
| ~ spl0_235
| spl0_522 ),
inference(forward_demodulation,[],[f7376,f2312]) ).
fof(f7376,plain,
( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
| spl0_522 ),
inference(avatar_component_clause,[],[f7375]) ).
fof(f7395,plain,
( ~ spl0_525
| ~ spl0_235
| spl0_523 ),
inference(avatar_split_clause,[],[f7383,f7379,f2310,f7392]) ).
fof(f7392,plain,
( spl0_525
<=> member(regular(complement(compose(element_relation,complement(singleton_relation)))),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f7379,plain,
( spl0_523
<=> member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f7383,plain,
( ~ member(regular(complement(compose(element_relation,complement(singleton_relation)))),element_relation)
| ~ spl0_235
| spl0_523 ),
inference(forward_demodulation,[],[f7381,f2312]) ).
fof(f7381,plain,
( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation)
| spl0_523 ),
inference(avatar_component_clause,[],[f7379]) ).
fof(f7390,plain,
( ~ spl0_524
| ~ spl0_235
| spl0_521 ),
inference(avatar_split_clause,[],[f7385,f7371,f2310,f7387]) ).
fof(f7387,plain,
( spl0_524
<=> null_class = complement(compose(element_relation,complement(singleton_relation))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f7385,plain,
( null_class != complement(compose(element_relation,complement(singleton_relation)))
| ~ spl0_235
| spl0_521 ),
inference(forward_demodulation,[],[f7372,f2312]) ).
fof(f7372,plain,
( null_class != complement(compose(element_relation,complement(identity_relation)))
| spl0_521 ),
inference(avatar_component_clause,[],[f7371]) ).
fof(f7382,plain,
( spl0_521
| spl0_522
| ~ spl0_523
| ~ spl0_23
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1196,f1163,f299,f7379,f7375,f7371]) ).
fof(f1196,plain,
( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation)
| member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
| null_class = complement(compose(element_relation,complement(identity_relation)))
| ~ spl0_23
| ~ spl0_143 ),
inference(resolution,[],[f1164,f300]) ).
fof(f7369,plain,
( spl0_520
| ~ spl0_129
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1185,f1159,f1008,f7367]) ).
fof(f7367,plain,
( spl0_520
<=> ! [X0,X1] :
( member(regular(intersection(X0,regular(X1))),null_class)
| ~ member(regular(intersection(X0,regular(X1))),X1)
| null_class = X1
| null_class = intersection(X0,regular(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f1185,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,regular(X1))),null_class)
| ~ member(regular(intersection(X0,regular(X1))),X1)
| null_class = X1
| null_class = intersection(X0,regular(X1)) )
| ~ spl0_129
| ~ spl0_142 ),
inference(resolution,[],[f1160,f1009]) ).
fof(f7365,plain,
( spl0_519
| ~ spl0_128
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1183,f1159,f1004,f7363]) ).
fof(f7363,plain,
( spl0_519
<=> ! [X0,X1] :
( member(regular(intersection(regular(X0),X1)),null_class)
| ~ member(regular(intersection(regular(X0),X1)),X0)
| null_class = X0
| null_class = intersection(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f1183,plain,
( ! [X0,X1] :
( member(regular(intersection(regular(X0),X1)),null_class)
| ~ member(regular(intersection(regular(X0),X1)),X0)
| null_class = X0
| null_class = intersection(regular(X0),X1) )
| ~ spl0_128
| ~ spl0_142 ),
inference(resolution,[],[f1160,f1005]) ).
fof(f7361,plain,
( spl0_518
| ~ spl0_48
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1044,f1008,f444,f7359]) ).
fof(f7359,plain,
( spl0_518
<=> ! [X2,X0,X1] :
( null_class = intersection(X0,unordered_pair(X1,X2))
| regular(intersection(X0,unordered_pair(X1,X2))) = X1
| regular(intersection(X0,unordered_pair(X1,X2))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f1044,plain,
( ! [X2,X0,X1] :
( null_class = intersection(X0,unordered_pair(X1,X2))
| regular(intersection(X0,unordered_pair(X1,X2))) = X1
| regular(intersection(X0,unordered_pair(X1,X2))) = X2 )
| ~ spl0_48
| ~ spl0_129 ),
inference(resolution,[],[f1009,f445]) ).
fof(f7357,plain,
( spl0_517
| ~ spl0_48
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1028,f1004,f444,f7355]) ).
fof(f7355,plain,
( spl0_517
<=> ! [X2,X0,X1] :
( null_class = intersection(unordered_pair(X0,X1),X2)
| regular(intersection(unordered_pair(X0,X1),X2)) = X0
| regular(intersection(unordered_pair(X0,X1),X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f1028,plain,
( ! [X2,X0,X1] :
( null_class = intersection(unordered_pair(X0,X1),X2)
| regular(intersection(unordered_pair(X0,X1),X2)) = X0
| regular(intersection(unordered_pair(X0,X1),X2)) = X1 )
| ~ spl0_48
| ~ spl0_128 ),
inference(resolution,[],[f1005,f445]) ).
fof(f7049,plain,
( spl0_516
| ~ spl0_61
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1714,f1711,f524,f7047]) ).
fof(f7047,plain,
( spl0_516
<=> ! [X0,X1] :
( ~ member(regular(cross_product(X0,X1)),element_relation)
| member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f1714,plain,
( ! [X0,X1] :
( ~ member(regular(cross_product(X0,X1)),element_relation)
| member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = null_class )
| ~ spl0_61
| ~ spl0_198 ),
inference(superposition,[],[f525,f1712]) ).
fof(f7037,plain,
( spl0_515
| ~ spl0_130
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1604,f1584,f1012,f7035]) ).
fof(f7035,plain,
( spl0_515
<=> ! [X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(X1,domain_of(X0)),not_subclass_element(X1,domain_of(X0))),universal_class))
| subclass(X1,domain_of(X0))
| ~ subclass(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f1604,plain,
( ! [X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(X1,domain_of(X0)),not_subclass_element(X1,domain_of(X0))),universal_class))
| subclass(X1,domain_of(X0))
| ~ subclass(X1,universal_class) )
| ~ spl0_130
| ~ spl0_187 ),
inference(duplicate_literal_removal,[],[f1603]) ).
fof(f1603,plain,
( ! [X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(X1,domain_of(X0)),not_subclass_element(X1,domain_of(X0))),universal_class))
| subclass(X1,domain_of(X0))
| ~ subclass(X1,universal_class)
| subclass(X1,domain_of(X0)) )
| ~ spl0_130
| ~ spl0_187 ),
inference(resolution,[],[f1585,f1013]) ).
fof(f7033,plain,
( ~ spl0_514
| ~ spl0_182
| spl0_192
| ~ spl0_12
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1563,f1556,f254,f1613,f1538,f7030]) ).
fof(f7030,plain,
( spl0_514
<=> inductive(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f1538,plain,
( spl0_182
<=> member(null_class,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1613,plain,
( spl0_192
<=> member(null_class,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1563,plain,
( member(null_class,subset_relation)
| ~ member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ spl0_12
| ~ spl0_185 ),
inference(resolution,[],[f1557,f255]) ).
fof(f7028,plain,
( spl0_513
| ~ spl0_31
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1502,f1456,f335,f7026]) ).
fof(f7026,plain,
( spl0_513
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f1502,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X0) )
| ~ spl0_31
| ~ spl0_171 ),
inference(resolution,[],[f1457,f336]) ).
fof(f7024,plain,
( spl0_512
| ~ spl0_32
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1501,f1456,f339,f7022]) ).
fof(f7022,plain,
( spl0_512
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f1501,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X1) )
| ~ spl0_32
| ~ spl0_171 ),
inference(resolution,[],[f1457,f340]) ).
fof(f7020,plain,
( spl0_511
| ~ spl0_31
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1484,f1452,f335,f7018]) ).
fof(f7018,plain,
( spl0_511
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ subclass(universal_class,intersection(X1,X2))
| ~ member(X3,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f1484,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,intersection(X1,X2))
| ~ member(X3,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X1) )
| ~ spl0_31
| ~ spl0_170 ),
inference(resolution,[],[f1453,f336]) ).
fof(f7016,plain,
( spl0_510
| ~ spl0_32
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1483,f1452,f339,f7014]) ).
fof(f7014,plain,
( spl0_510
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ subclass(universal_class,intersection(X1,X2))
| ~ member(X3,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f1483,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,intersection(X1,X2))
| ~ member(X3,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X2) )
| ~ spl0_32
| ~ spl0_170 ),
inference(resolution,[],[f1453,f340]) ).
fof(f7012,plain,
( spl0_509
| ~ spl0_38
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1422,f1369,f372,f7010]) ).
fof(f7010,plain,
( spl0_509
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f1422,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X2) )
| ~ spl0_38
| ~ spl0_165 ),
inference(resolution,[],[f1370,f373]) ).
fof(f7008,plain,
( spl0_508
| ~ spl0_142
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1346,f1316,f1159,f7006]) ).
fof(f7006,plain,
( spl0_508
<=> ! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,null_class)
| ~ member(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f1346,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,null_class)
| ~ member(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_142
| ~ spl0_160 ),
inference(duplicate_literal_removal,[],[f1325]) ).
fof(f1325,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,null_class)
| ~ member(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class )
| ~ spl0_142
| ~ spl0_160 ),
inference(superposition,[],[f1160,f1317]) ).
fof(f7004,plain,
( spl0_507
| ~ spl0_142
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1341,f1316,f1159,f7002]) ).
fof(f7002,plain,
( spl0_507
<=> ! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,null_class)
| ~ member(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f1341,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,null_class)
| ~ member(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_142
| ~ spl0_160 ),
inference(duplicate_literal_removal,[],[f1330]) ).
fof(f1330,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,null_class)
| ~ member(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class )
| ~ spl0_142
| ~ spl0_160 ),
inference(superposition,[],[f1160,f1317]) ).
fof(f6992,plain,
( spl0_506
| ~ spl0_49
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f967,f915,f448,f6990]) ).
fof(f6990,plain,
( spl0_506
<=> ! [X2,X0,X1] :
( subclass(complement(intersection(X0,X1)),X2)
| ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X1)
| ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f967,plain,
( ! [X2,X0,X1] :
( subclass(complement(intersection(X0,X1)),X2)
| ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X1)
| ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X0) )
| ~ spl0_49
| ~ spl0_115 ),
inference(resolution,[],[f916,f449]) ).
fof(f6844,plain,
( spl0_505
| ~ spl0_235
| ~ spl0_497 ),
inference(avatar_split_clause,[],[f6806,f6803,f2310,f6842]) ).
fof(f6842,plain,
( spl0_505
<=> ! [X0] :
( member(X0,singleton_relation)
| null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,subset_relation)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f6803,plain,
( spl0_497
<=> ! [X0] :
( null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,subset_relation)
| member(X0,identity_relation)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f6806,plain,
( ! [X0] :
( member(X0,singleton_relation)
| null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,subset_relation)
| ~ member(X0,universal_class) )
| ~ spl0_235
| ~ spl0_497 ),
inference(forward_demodulation,[],[f6804,f2312]) ).
fof(f6804,plain,
( ! [X0] :
( null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,subset_relation)
| member(X0,identity_relation)
| ~ member(X0,universal_class) )
| ~ spl0_497 ),
inference(avatar_component_clause,[],[f6803]) ).
fof(f6834,plain,
( spl0_504
| ~ spl0_68
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1875,f1868,f560,f6832]) ).
fof(f6832,plain,
( spl0_504
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,cross_product(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f1875,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,cross_product(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(X2,X0) )
| ~ spl0_68
| ~ spl0_205 ),
inference(resolution,[],[f1869,f561]) ).
fof(f6830,plain,
( spl0_503
| ~ spl0_20
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1503,f1456,f287,f6828]) ).
fof(f6828,plain,
( spl0_503
<=> ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f1503,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0) )
| ~ spl0_20
| ~ spl0_171 ),
inference(resolution,[],[f1457,f288]) ).
fof(f6826,plain,
( spl0_502
| ~ spl0_20
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1485,f1452,f287,f6824]) ).
fof(f6824,plain,
( spl0_502
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,complement(X1))
| ~ member(X2,universal_class)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f1485,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,complement(X1))
| ~ member(X2,universal_class)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1) )
| ~ spl0_20
| ~ spl0_170 ),
inference(resolution,[],[f1453,f288]) ).
fof(f6822,plain,
( spl0_501
| ~ spl0_31
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1426,f1369,f335,f6820]) ).
fof(f6820,plain,
( spl0_501
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f1426,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X0) )
| ~ spl0_31
| ~ spl0_165 ),
inference(resolution,[],[f1370,f336]) ).
fof(f6818,plain,
( spl0_500
| ~ spl0_32
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1425,f1369,f339,f6816]) ).
fof(f6816,plain,
( spl0_500
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f1425,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X1) )
| ~ spl0_32
| ~ spl0_165 ),
inference(resolution,[],[f1370,f340]) ).
fof(f6814,plain,
( spl0_499
| ~ spl0_109
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1382,f1361,f815,f6812]) ).
fof(f6812,plain,
( spl0_499
<=> ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| member(null_class,X2)
| ~ inductive(unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f815,plain,
( spl0_109
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| member(null_class,X1)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1382,plain,
( ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| member(null_class,X2)
| ~ inductive(unordered_pair(X0,X1)) )
| ~ spl0_109
| ~ spl0_163 ),
inference(resolution,[],[f1362,f816]) ).
fof(f816,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| member(null_class,X1)
| ~ inductive(X0) )
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f815]) ).
fof(f6810,plain,
( spl0_498
| ~ spl0_38
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1356,f1351,f372,f6808]) ).
fof(f6808,plain,
( spl0_498
<=> ! [X0,X1] :
( ~ member(X0,subset_relation)
| ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X1)
| member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f1356,plain,
( ! [X0,X1] :
( ~ member(X0,subset_relation)
| ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X1)
| member(X0,X1) )
| ~ spl0_38
| ~ spl0_162 ),
inference(resolution,[],[f1352,f373]) ).
fof(f6805,plain,
( spl0_497
| ~ spl0_50
| ~ spl0_70
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1217,f1167,f568,f452,f6803]) ).
fof(f1217,plain,
( ! [X0] :
( null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,subset_relation)
| member(X0,identity_relation)
| ~ member(X0,universal_class) )
| ~ spl0_50
| ~ spl0_70
| ~ spl0_144 ),
inference(forward_demodulation,[],[f1204,f453]) ).
fof(f1204,plain,
( ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,identity_relation)
| ~ member(X0,universal_class)
| null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),flip(cross_product(subset_relation,universal_class))) )
| ~ spl0_70
| ~ spl0_144 ),
inference(resolution,[],[f1168,f569]) ).
fof(f6599,plain,
( spl0_496
| ~ spl0_235
| ~ spl0_483 ),
inference(avatar_split_clause,[],[f6418,f6415,f2310,f6597]) ).
fof(f6597,plain,
( spl0_496
<=> ! [X0,X1] :
( member(not_subclass_element(X0,X1),singleton_relation)
| ~ member(not_subclass_element(X0,X1),subset_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f6415,plain,
( spl0_483
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),subset_relation)
| member(not_subclass_element(X0,X1),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f6418,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,X1),singleton_relation)
| ~ member(not_subclass_element(X0,X1),subset_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(X0,X1) )
| ~ spl0_235
| ~ spl0_483 ),
inference(forward_demodulation,[],[f6416,f2312]) ).
fof(f6416,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),subset_relation)
| member(not_subclass_element(X0,X1),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(X0,X1) )
| ~ spl0_483 ),
inference(avatar_component_clause,[],[f6415]) ).
fof(f6595,plain,
( spl0_495
| ~ spl0_235
| ~ spl0_482 ),
inference(avatar_split_clause,[],[f6413,f6410,f2310,f6593]) ).
fof(f6593,plain,
( spl0_495
<=> ! [X0,X1] :
( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
| ~ member(not_subclass_element(X0,X1),element_relation)
| member(not_subclass_element(X0,X1),singleton_relation)
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f6410,plain,
( spl0_482
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),element_relation)
| member(not_subclass_element(X0,X1),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f6413,plain,
( ! [X0,X1] :
( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
| ~ member(not_subclass_element(X0,X1),element_relation)
| member(not_subclass_element(X0,X1),singleton_relation)
| subclass(X0,X1) )
| ~ spl0_235
| ~ spl0_482 ),
inference(forward_demodulation,[],[f6411,f2312]) ).
fof(f6411,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),element_relation)
| member(not_subclass_element(X0,X1),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| subclass(X0,X1) )
| ~ spl0_482 ),
inference(avatar_component_clause,[],[f6410]) ).
fof(f6463,plain,
( spl0_493
| ~ spl0_494
| ~ spl0_86
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1872,f1868,f669,f6460,f6457]) ).
fof(f6457,plain,
( spl0_493
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f6460,plain,
( spl0_494
<=> subclass(composition_function,application_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f1872,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,application_function)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(X1,domain_of(X0)) )
| ~ spl0_86
| ~ spl0_205 ),
inference(resolution,[],[f1869,f670]) ).
fof(f6455,plain,
( spl0_492
| ~ spl0_68
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1717,f1711,f560,f6453]) ).
fof(f6453,plain,
( spl0_492
<=> ! [X0,X3,X2,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
| member(first(regular(cross_product(X0,X1))),X2)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f1717,plain,
( ! [X2,X3,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
| member(first(regular(cross_product(X0,X1))),X2)
| cross_product(X0,X1) = null_class )
| ~ spl0_68
| ~ spl0_198 ),
inference(superposition,[],[f561,f1712]) ).
fof(f6451,plain,
( spl0_491
| ~ spl0_67
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1716,f1711,f556,f6449]) ).
fof(f6449,plain,
( spl0_491
<=> ! [X0,X3,X2,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
| member(second(regular(cross_product(X0,X1))),X3)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f1716,plain,
( ! [X2,X3,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
| member(second(regular(cross_product(X0,X1))),X3)
| cross_product(X0,X1) = null_class )
| ~ spl0_67
| ~ spl0_198 ),
inference(superposition,[],[f557,f1712]) ).
fof(f6447,plain,
( spl0_490
| ~ spl0_22
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1440,f1373,f295,f6445]) ).
fof(f6445,plain,
( spl0_490
<=> ! [X0,X1] :
( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
| ~ member(X0,universal_class)
| member(X0,cross_product(universal_class,universal_class))
| ~ function(domain_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f1440,plain,
( ! [X0,X1] :
( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
| ~ member(X0,universal_class)
| member(X0,cross_product(universal_class,universal_class))
| ~ function(domain_of(X1)) )
| ~ spl0_22
| ~ spl0_166 ),
inference(resolution,[],[f1374,f296]) ).
fof(f6443,plain,
( spl0_489
| ~ spl0_20
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1427,f1369,f287,f6441]) ).
fof(f1427,plain,
( ! [X0,X1] :
( ~ subclass(domain_relation,complement(X0))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0) )
| ~ spl0_20
| ~ spl0_165 ),
inference(resolution,[],[f1370,f288]) ).
fof(f6439,plain,
( spl0_488
| ~ spl0_131
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1381,f1361,f1016,f6437]) ).
fof(f6437,plain,
( spl0_488
<=> ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| member(X0,X2)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f1381,plain,
( ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| member(X0,X2)
| ~ member(X0,universal_class) )
| ~ spl0_131
| ~ spl0_163 ),
inference(resolution,[],[f1362,f1017]) ).
fof(f6435,plain,
( spl0_487
| ~ spl0_132
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1380,f1361,f1020,f6433]) ).
fof(f6433,plain,
( spl0_487
<=> ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| member(X1,X2)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f1380,plain,
( ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| member(X1,X2)
| ~ member(X1,universal_class) )
| ~ spl0_132
| ~ spl0_163 ),
inference(resolution,[],[f1362,f1021]) ).
fof(f6431,plain,
( ~ spl0_485
| spl0_486
| ~ spl0_114
| ~ spl0_398 ),
inference(avatar_split_clause,[],[f6328,f4364,f892,f6428,f6424]) ).
fof(f6424,plain,
( spl0_485
<=> single_valued_class(singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f6428,plain,
( spl0_486
<=> function(singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f4364,plain,
( spl0_398
<=> subclass(singleton_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f6328,plain,
( function(singleton_relation)
| ~ single_valued_class(singleton_relation)
| ~ spl0_114
| ~ spl0_398 ),
inference(resolution,[],[f4366,f893]) ).
fof(f4366,plain,
( subclass(singleton_relation,cross_product(universal_class,universal_class))
| ~ spl0_398 ),
inference(avatar_component_clause,[],[f4364]) ).
fof(f6422,plain,
( spl0_484
| ~ spl0_38
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1347,f1320,f372,f6420]) ).
fof(f6420,plain,
( spl0_484
<=> ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ function(X1)
| ~ subclass(universal_class,X2)
| member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f1320,plain,
( spl0_161
<=> ! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ member(X0,universal_class)
| ~ function(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1347,plain,
( ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ function(X1)
| ~ subclass(universal_class,X2)
| member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),X2) )
| ~ spl0_38
| ~ spl0_161 ),
inference(resolution,[],[f1321,f373]) ).
fof(f1321,plain,
( ! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ member(X0,universal_class)
| ~ function(X1) )
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f1320]) ).
fof(f6417,plain,
( spl0_483
| ~ spl0_130
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1216,f1167,f1012,f6415]) ).
fof(f1216,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),subset_relation)
| member(not_subclass_element(X0,X1),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(X0,X1) )
| ~ spl0_130
| ~ spl0_144 ),
inference(resolution,[],[f1168,f1013]) ).
fof(f6412,plain,
( spl0_482
| ~ spl0_130
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1202,f1163,f1012,f6410]) ).
fof(f1202,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),element_relation)
| member(not_subclass_element(X0,X1),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| subclass(X0,X1) )
| ~ spl0_130
| ~ spl0_143 ),
inference(resolution,[],[f1164,f1013]) ).
fof(f6408,plain,
( spl0_481
| ~ spl0_130
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1188,f1159,f1012,f6406]) ).
fof(f6406,plain,
( spl0_481
<=> ! [X2,X0,X1] :
( member(not_subclass_element(X0,X1),null_class)
| ~ member(not_subclass_element(X0,X1),X2)
| null_class = X2
| ~ subclass(X0,regular(X2))
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f1188,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(X0,X1),null_class)
| ~ member(not_subclass_element(X0,X1),X2)
| null_class = X2
| ~ subclass(X0,regular(X2))
| subclass(X0,X1) )
| ~ spl0_130
| ~ spl0_142 ),
inference(resolution,[],[f1160,f1013]) ).
fof(f6404,plain,
( spl0_480
| ~ spl0_76
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1143,f1087,f608,f6402]) ).
fof(f6402,plain,
( spl0_480
<=> ! [X0] :
( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subclass(subset_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f1143,plain,
( ! [X0] :
( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subclass(subset_relation,X0) )
| ~ spl0_76
| ~ spl0_135 ),
inference(superposition,[],[f1088,f610]) ).
fof(f6400,plain,
( spl0_479
| ~ spl0_49
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f896,f884,f448,f6398]) ).
fof(f6398,plain,
( spl0_479
<=> ! [X0,X1] :
( complement(intersection(X0,X1)) = null_class
| ~ member(regular(complement(intersection(X0,X1))),X1)
| ~ member(regular(complement(intersection(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f896,plain,
( ! [X0,X1] :
( complement(intersection(X0,X1)) = null_class
| ~ member(regular(complement(intersection(X0,X1))),X1)
| ~ member(regular(complement(intersection(X0,X1))),X0) )
| ~ spl0_49
| ~ spl0_112 ),
inference(resolution,[],[f885,f449]) ).
fof(f6236,plain,
( spl0_478
| ~ spl0_27
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1607,f1584,f319,f6234]) ).
fof(f6234,plain,
( spl0_478
<=> ! [X0] :
( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class))
| subclass(universal_class,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f1607,plain,
( ! [X0] :
( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class))
| subclass(universal_class,domain_of(X0)) )
| ~ spl0_27
| ~ spl0_187 ),
inference(duplicate_literal_removal,[],[f1600]) ).
fof(f1600,plain,
( ! [X0] :
( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class))
| subclass(universal_class,domain_of(X0))
| subclass(universal_class,domain_of(X0)) )
| ~ spl0_27
| ~ spl0_187 ),
inference(resolution,[],[f1585,f320]) ).
fof(f6232,plain,
( spl0_477
| ~ spl0_49
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1576,f1556,f448,f6230]) ).
fof(f6230,plain,
( spl0_477
<=> ! [X0] :
( member(X0,subset_relation)
| ~ member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f1576,plain,
( ! [X0] :
( member(X0,subset_relation)
| ~ member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) )
| ~ spl0_49
| ~ spl0_185 ),
inference(duplicate_literal_removal,[],[f1560]) ).
fof(f1560,plain,
( ! [X0] :
( member(X0,subset_relation)
| ~ member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ~ member(X0,cross_product(universal_class,universal_class)) )
| ~ spl0_49
| ~ spl0_185 ),
inference(resolution,[],[f1557,f449]) ).
fof(f6228,plain,
( ~ spl0_476
| ~ spl0_235
| spl0_475 ),
inference(avatar_split_clause,[],[f6223,f6219,f2310,f6225]) ).
fof(f6225,plain,
( spl0_476
<=> subclass(domain_relation,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f6219,plain,
( spl0_475
<=> subclass(domain_relation,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f6223,plain,
( ~ subclass(domain_relation,singleton_relation)
| ~ spl0_235
| spl0_475 ),
inference(forward_demodulation,[],[f6221,f2312]) ).
fof(f6221,plain,
( ~ subclass(domain_relation,identity_relation)
| spl0_475 ),
inference(avatar_component_clause,[],[f6219]) ).
fof(f6222,plain,
( spl0_474
| ~ spl0_475
| ~ spl0_103
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1433,f1369,f761,f6219,f6216]) ).
fof(f6216,plain,
( spl0_474
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f1433,plain,
( ! [X0] :
( ~ subclass(domain_relation,identity_relation)
| ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation) )
| ~ spl0_103
| ~ spl0_165 ),
inference(resolution,[],[f1370,f762]) ).
fof(f6214,plain,
( spl0_473
| ~ spl0_116
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1344,f1316,f919,f6212]) ).
fof(f6212,plain,
( spl0_473
<=> ! [X2,X0,X1] :
( member(X1,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f1344,plain,
( ! [X2,X0,X1] :
( member(X1,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_116
| ~ spl0_160 ),
inference(duplicate_literal_removal,[],[f1327]) ).
fof(f1327,plain,
( ! [X2,X0,X1] :
( member(X1,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class )
| ~ spl0_116
| ~ spl0_160 ),
inference(superposition,[],[f920,f1317]) ).
fof(f6210,plain,
( spl0_472
| ~ spl0_116
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1339,f1316,f919,f6208]) ).
fof(f6208,plain,
( spl0_472
<=> ! [X2,X0,X1] :
( member(X0,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f1339,plain,
( ! [X2,X0,X1] :
( member(X0,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_116
| ~ spl0_160 ),
inference(duplicate_literal_removal,[],[f1332]) ).
fof(f1332,plain,
( ! [X2,X0,X1] :
( member(X0,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class )
| ~ spl0_116
| ~ spl0_160 ),
inference(superposition,[],[f920,f1317]) ).
fof(f6206,plain,
( spl0_471
| ~ spl0_27
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1178,f1159,f319,f6204]) ).
fof(f6204,plain,
( spl0_471
<=> ! [X0,X1] :
( member(not_subclass_element(regular(X0),X1),null_class)
| ~ member(not_subclass_element(regular(X0),X1),X0)
| null_class = X0
| subclass(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f1178,plain,
( ! [X0,X1] :
( member(not_subclass_element(regular(X0),X1),null_class)
| ~ member(not_subclass_element(regular(X0),X1),X0)
| null_class = X0
| subclass(regular(X0),X1) )
| ~ spl0_27
| ~ spl0_142 ),
inference(resolution,[],[f1160,f320]) ).
fof(f6194,plain,
( spl0_274
| spl0_470
| ~ spl0_76
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1056,f1008,f608,f6191,f2535]) ).
fof(f1056,plain,
( member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| null_class = subset_relation
| ~ spl0_76
| ~ spl0_129 ),
inference(superposition,[],[f1009,f610]) ).
fof(f6189,plain,
( spl0_469
| ~ spl0_44
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f968,f915,f424,f6187]) ).
fof(f6187,plain,
( spl0_469
<=> ! [X0,X1] :
( subclass(complement(complement(X0)),X1)
| member(not_subclass_element(complement(complement(X0)),X1),X0)
| ~ member(not_subclass_element(complement(complement(X0)),X1),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f968,plain,
( ! [X0,X1] :
( subclass(complement(complement(X0)),X1)
| member(not_subclass_element(complement(complement(X0)),X1),X0)
| ~ member(not_subclass_element(complement(complement(X0)),X1),universal_class) )
| ~ spl0_44
| ~ spl0_115 ),
inference(resolution,[],[f916,f425]) ).
fof(f6185,plain,
( spl0_468
| ~ spl0_79
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f875,f823,f628,f6183]) ).
fof(f6183,plain,
( spl0_468
<=> ! [X0] :
( ~ member(X0,subset_relation)
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f875,plain,
( ! [X0] :
( ~ member(X0,subset_relation)
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
| ~ spl0_79
| ~ spl0_111 ),
inference(resolution,[],[f824,f629]) ).
fof(f6180,plain,
( spl0_466
| ~ spl0_467
| ~ spl0_85
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f828,f802,f664,f6177,f6174]) ).
fof(f6174,plain,
( spl0_466
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f6177,plain,
( spl0_467
<=> subclass(universal_class,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f828,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1) )
| ~ spl0_85
| ~ spl0_106 ),
inference(resolution,[],[f803,f665]) ).
fof(f6022,plain,
( spl0_465
| ~ spl0_235
| ~ spl0_457 ),
inference(avatar_split_clause,[],[f5904,f5901,f2310,f6020]) ).
fof(f6020,plain,
( spl0_465
<=> ! [X0] :
( member(regular(X0),singleton_relation)
| ~ member(regular(X0),subset_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f5901,plain,
( spl0_457
<=> ! [X0] :
( ~ member(regular(X0),subset_relation)
| member(regular(X0),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f5904,plain,
( ! [X0] :
( member(regular(X0),singleton_relation)
| ~ member(regular(X0),subset_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| null_class = X0 )
| ~ spl0_235
| ~ spl0_457 ),
inference(forward_demodulation,[],[f5902,f2312]) ).
fof(f5902,plain,
( ! [X0] :
( ~ member(regular(X0),subset_relation)
| member(regular(X0),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| null_class = X0 )
| ~ spl0_457 ),
inference(avatar_component_clause,[],[f5901]) ).
fof(f6018,plain,
( spl0_464
| ~ spl0_235
| ~ spl0_456 ),
inference(avatar_split_clause,[],[f5899,f5896,f2310,f6016]) ).
fof(f6016,plain,
( spl0_464
<=> ! [X0] :
( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
| ~ member(regular(X0),element_relation)
| member(regular(X0),singleton_relation)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f5896,plain,
( spl0_456
<=> ! [X0] :
( ~ member(regular(X0),element_relation)
| member(regular(X0),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f5899,plain,
( ! [X0] :
( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
| ~ member(regular(X0),element_relation)
| member(regular(X0),singleton_relation)
| null_class = X0 )
| ~ spl0_235
| ~ spl0_456 ),
inference(forward_demodulation,[],[f5897,f2312]) ).
fof(f5897,plain,
( ! [X0] :
( ~ member(regular(X0),element_relation)
| member(regular(X0),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| null_class = X0 )
| ~ spl0_456 ),
inference(avatar_component_clause,[],[f5896]) ).
fof(f5929,plain,
( spl0_463
| ~ spl0_235
| ~ spl0_453 ),
inference(avatar_split_clause,[],[f5886,f5883,f2310,f5927]) ).
fof(f5927,plain,
( spl0_463
<=> ! [X0] :
( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),singleton_relation)
| subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f5883,plain,
( spl0_453
<=> ! [X0] :
( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),identity_relation)
| subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f5886,plain,
( ! [X0] :
( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),singleton_relation)
| subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) )
| ~ spl0_235
| ~ spl0_453 ),
inference(forward_demodulation,[],[f5884,f2312]) ).
fof(f5884,plain,
( ! [X0] :
( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),identity_relation)
| subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) )
| ~ spl0_453 ),
inference(avatar_component_clause,[],[f5883]) ).
fof(f5925,plain,
( spl0_462
| ~ spl0_235
| ~ spl0_452 ),
inference(avatar_split_clause,[],[f5881,f5877,f2310,f5923]) ).
fof(f5923,plain,
( spl0_462
<=> ! [X0] :
( subclass(complement(complement(compose(element_relation,complement(singleton_relation)))),X0)
| ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(singleton_relation)))),X0),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f5877,plain,
( spl0_452
<=> ! [X0] :
( ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(identity_relation)))),X0),singleton_relation)
| subclass(complement(complement(compose(element_relation,complement(identity_relation)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f5881,plain,
( ! [X0] :
( subclass(complement(complement(compose(element_relation,complement(singleton_relation)))),X0)
| ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(singleton_relation)))),X0),singleton_relation) )
| ~ spl0_235
| ~ spl0_452 ),
inference(forward_demodulation,[],[f5880,f2312]) ).
fof(f5880,plain,
( ! [X0] :
( ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(singleton_relation)))),X0),singleton_relation)
| subclass(complement(complement(compose(element_relation,complement(identity_relation)))),X0) )
| ~ spl0_235
| ~ spl0_452 ),
inference(forward_demodulation,[],[f5878,f2312]) ).
fof(f5878,plain,
( ! [X0] :
( ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(identity_relation)))),X0),singleton_relation)
| subclass(complement(complement(compose(element_relation,complement(identity_relation)))),X0) )
| ~ spl0_452 ),
inference(avatar_component_clause,[],[f5877]) ).
fof(f5921,plain,
( spl0_461
| ~ spl0_40
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1343,f1316,f380,f5919]) ).
fof(f5919,plain,
( spl0_461
<=> ! [X0,X1] :
( null_class = intersection(unordered_pair(X0,X1),X1)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f1343,plain,
( ! [X0,X1] :
( null_class = intersection(unordered_pair(X0,X1),X1)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_40
| ~ spl0_160 ),
inference(duplicate_literal_removal,[],[f1328]) ).
fof(f1328,plain,
( ! [X0,X1] :
( null_class = intersection(unordered_pair(X0,X1),X1)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class )
| ~ spl0_40
| ~ spl0_160 ),
inference(superposition,[],[f381,f1317]) ).
fof(f5917,plain,
( ~ spl0_459
| spl0_460
| ~ spl0_114
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f5810,f4206,f892,f5914,f5910]) ).
fof(f5910,plain,
( spl0_459
<=> single_valued_class(subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f5914,plain,
( spl0_460
<=> function(subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f4206,plain,
( spl0_383
<=> subclass(subset_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f5810,plain,
( function(subset_relation)
| ~ single_valued_class(subset_relation)
| ~ spl0_114
| ~ spl0_383 ),
inference(resolution,[],[f4208,f893]) ).
fof(f4208,plain,
( subclass(subset_relation,cross_product(universal_class,universal_class))
| ~ spl0_383 ),
inference(avatar_component_clause,[],[f4206]) ).
fof(f5908,plain,
( spl0_458
| ~ spl0_40
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1338,f1316,f380,f5906]) ).
fof(f5906,plain,
( spl0_458
<=> ! [X0,X1] :
( null_class = intersection(unordered_pair(X0,X1),X0)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f1338,plain,
( ! [X0,X1] :
( null_class = intersection(unordered_pair(X0,X1),X0)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_40
| ~ spl0_160 ),
inference(duplicate_literal_removal,[],[f1333]) ).
fof(f1333,plain,
( ! [X0,X1] :
( null_class = intersection(unordered_pair(X0,X1),X0)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class )
| ~ spl0_40
| ~ spl0_160 ),
inference(superposition,[],[f381,f1317]) ).
fof(f5903,plain,
( spl0_457
| ~ spl0_116
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1212,f1167,f919,f5901]) ).
fof(f1212,plain,
( ! [X0] :
( ~ member(regular(X0),subset_relation)
| member(regular(X0),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| null_class = X0 )
| ~ spl0_116
| ~ spl0_144 ),
inference(resolution,[],[f1168,f920]) ).
fof(f5898,plain,
( spl0_456
| ~ spl0_116
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1198,f1163,f919,f5896]) ).
fof(f1198,plain,
( ! [X0] :
( ~ member(regular(X0),element_relation)
| member(regular(X0),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| null_class = X0 )
| ~ spl0_116
| ~ spl0_143 ),
inference(resolution,[],[f1164,f920]) ).
fof(f5894,plain,
( spl0_455
| ~ spl0_116
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1184,f1159,f919,f5892]) ).
fof(f5892,plain,
( spl0_455
<=> ! [X0,X1] :
( member(regular(X0),null_class)
| ~ member(regular(X0),X1)
| null_class = X1
| ~ subclass(X0,regular(X1))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f1184,plain,
( ! [X0,X1] :
( member(regular(X0),null_class)
| ~ member(regular(X0),X1)
| null_class = X1
| ~ subclass(X0,regular(X1))
| null_class = X0 )
| ~ spl0_116
| ~ spl0_142 ),
inference(resolution,[],[f1160,f920]) ).
fof(f5890,plain,
( spl0_454
| ~ spl0_48
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1062,f1012,f444,f5888]) ).
fof(f5888,plain,
( spl0_454
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| subclass(X0,X3)
| not_subclass_element(X0,X3) = X1
| not_subclass_element(X0,X3) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f1062,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| subclass(X0,X3)
| not_subclass_element(X0,X3) = X1
| not_subclass_element(X0,X3) = X2 )
| ~ spl0_48
| ~ spl0_130 ),
inference(resolution,[],[f1013,f445]) ).
fof(f5885,plain,
( spl0_453
| ~ spl0_115
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f999,f959,f915,f5883]) ).
fof(f999,plain,
( ! [X0] :
( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),identity_relation)
| subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) )
| ~ spl0_115
| ~ spl0_125 ),
inference(resolution,[],[f960,f916]) ).
fof(f5879,plain,
( spl0_452
| ~ spl0_115
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f995,f955,f915,f5877]) ).
fof(f995,plain,
( ! [X0] :
( ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(identity_relation)))),X0),singleton_relation)
| subclass(complement(complement(compose(element_relation,complement(identity_relation)))),X0) )
| ~ spl0_115
| ~ spl0_124 ),
inference(resolution,[],[f956,f916]) ).
fof(f5818,plain,
( spl0_451
| ~ spl0_235
| ~ spl0_446 ),
inference(avatar_split_clause,[],[f5566,f5561,f2310,f5816]) ).
fof(f5816,plain,
( spl0_451
<=> ! [X0] :
( subclass(X0,singleton_relation)
| ~ member(not_subclass_element(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(not_subclass_element(X0,singleton_relation),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f5561,plain,
( spl0_446
<=> ! [X0] :
( ~ member(not_subclass_element(X0,identity_relation),subset_relation)
| ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f5566,plain,
( ! [X0] :
( subclass(X0,singleton_relation)
| ~ member(not_subclass_element(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(not_subclass_element(X0,singleton_relation),subset_relation) )
| ~ spl0_235
| ~ spl0_446 ),
inference(forward_demodulation,[],[f5565,f2312]) ).
fof(f5565,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(not_subclass_element(X0,singleton_relation),subset_relation)
| subclass(X0,identity_relation) )
| ~ spl0_235
| ~ spl0_446 ),
inference(forward_demodulation,[],[f5564,f2312]) ).
fof(f5564,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,singleton_relation),subset_relation)
| ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(X0,identity_relation) )
| ~ spl0_235
| ~ spl0_446 ),
inference(forward_demodulation,[],[f5562,f2312]) ).
fof(f5562,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,identity_relation),subset_relation)
| ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(X0,identity_relation) )
| ~ spl0_446 ),
inference(avatar_component_clause,[],[f5561]) ).
fof(f5809,plain,
( spl0_450
| ~ spl0_235
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f5559,f5556,f2310,f5807]) ).
fof(f5807,plain,
( spl0_450
<=> ! [X0] :
( ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
| ~ member(not_subclass_element(X0,singleton_relation),element_relation)
| subclass(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f5556,plain,
( spl0_445
<=> ! [X0] :
( ~ member(not_subclass_element(X0,singleton_relation),element_relation)
| ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(identity_relation))))
| subclass(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f5559,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
| ~ member(not_subclass_element(X0,singleton_relation),element_relation)
| subclass(X0,singleton_relation) )
| ~ spl0_235
| ~ spl0_445 ),
inference(forward_demodulation,[],[f5557,f2312]) ).
fof(f5557,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,singleton_relation),element_relation)
| ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(identity_relation))))
| subclass(X0,singleton_relation) )
| ~ spl0_445 ),
inference(avatar_component_clause,[],[f5556]) ).
fof(f5578,plain,
( spl0_448
| ~ spl0_449
| ~ spl0_78
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1414,f1369,f624,f5575,f5572]) ).
fof(f5572,plain,
( spl0_448
<=> ! [X0] :
( ~ member(X0,universal_class)
| domain_of(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f5575,plain,
( spl0_449
<=> subclass(domain_relation,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f1414,plain,
( ! [X0] :
( ~ subclass(domain_relation,successor_relation)
| ~ member(X0,universal_class)
| domain_of(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) )
| ~ spl0_78
| ~ spl0_165 ),
inference(resolution,[],[f1370,f625]) ).
fof(f5570,plain,
( spl0_447
| ~ spl0_28
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f3452,f3332,f323,f5568]) ).
fof(f5568,plain,
( spl0_447
<=> ! [X0] : subclass(intersection(X0,singleton_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f3452,plain,
( ! [X0] : subclass(intersection(X0,singleton_relation),subset_relation)
| ~ spl0_28
| ~ spl0_335 ),
inference(duplicate_literal_removal,[],[f3439]) ).
fof(f3439,plain,
( ! [X0] :
( subclass(intersection(X0,singleton_relation),subset_relation)
| subclass(intersection(X0,singleton_relation),subset_relation) )
| ~ spl0_28
| ~ spl0_335 ),
inference(resolution,[],[f3333,f324]) ).
fof(f5563,plain,
( spl0_446
| ~ spl0_43
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1403,f1365,f393,f5561]) ).
fof(f1403,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,identity_relation),subset_relation)
| ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(X0,identity_relation) )
| ~ spl0_43
| ~ spl0_164 ),
inference(superposition,[],[f1366,f395]) ).
fof(f5558,plain,
( spl0_445
| ~ spl0_41
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1402,f1365,f384,f5556]) ).
fof(f1402,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,singleton_relation),element_relation)
| ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(identity_relation))))
| subclass(X0,singleton_relation) )
| ~ spl0_41
| ~ spl0_164 ),
inference(superposition,[],[f1366,f386]) ).
fof(f5554,plain,
( spl0_444
| ~ spl0_40
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1398,f1365,f380,f5552]) ).
fof(f5552,plain,
( spl0_444
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X1,null_class),regular(X0))
| ~ member(not_subclass_element(X1,null_class),X0)
| subclass(X1,null_class)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f1398,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X1,null_class),regular(X0))
| ~ member(not_subclass_element(X1,null_class),X0)
| subclass(X1,null_class)
| null_class = X0 )
| ~ spl0_40
| ~ spl0_164 ),
inference(superposition,[],[f1366,f381]) ).
fof(f5550,plain,
( spl0_443
| ~ spl0_123
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1345,f1316,f951,f5548]) ).
fof(f5548,plain,
( spl0_443
<=> ! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,null_class)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f1345,plain,
( ! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,null_class)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_123
| ~ spl0_160 ),
inference(duplicate_literal_removal,[],[f1326]) ).
fof(f1326,plain,
( ! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,null_class)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class )
| ~ spl0_123
| ~ spl0_160 ),
inference(superposition,[],[f952,f1317]) ).
fof(f5546,plain,
( spl0_442
| ~ spl0_123
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1340,f1316,f951,f5544]) ).
fof(f5544,plain,
( spl0_442
<=> ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,null_class)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f1340,plain,
( ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,null_class)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_123
| ~ spl0_160 ),
inference(duplicate_literal_removal,[],[f1331]) ).
fof(f1331,plain,
( ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,null_class)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class )
| ~ spl0_123
| ~ spl0_160 ),
inference(superposition,[],[f952,f1317]) ).
fof(f5542,plain,
( spl0_441
| ~ spl0_38
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1259,f1247,f372,f5540]) ).
fof(f5540,plain,
( spl0_441
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f1259,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X2) )
| ~ spl0_38
| ~ spl0_152 ),
inference(resolution,[],[f1248,f373]) ).
fof(f5538,plain,
( ~ spl0_439
| spl0_440
| ~ spl0_106
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1215,f1167,f802,f5536,f5532]) ).
fof(f5532,plain,
( spl0_439
<=> subclass(universal_class,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f5536,plain,
( spl0_440
<=> ! [X0,X1] :
( ~ member(unordered_pair(X0,X1),subset_relation)
| member(unordered_pair(X0,X1),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f1215,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(X0,X1),subset_relation)
| member(unordered_pair(X0,X1),identity_relation)
| ~ subclass(universal_class,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_106
| ~ spl0_144 ),
inference(resolution,[],[f1168,f803]) ).
fof(f5530,plain,
( ~ spl0_438
| ~ spl0_235
| spl0_435 ),
inference(avatar_split_clause,[],[f5521,f5514,f2310,f5527]) ).
fof(f5527,plain,
( spl0_438
<=> subclass(universal_class,complement(compose(element_relation,complement(singleton_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f5521,plain,
( ~ subclass(universal_class,complement(compose(element_relation,complement(singleton_relation))))
| ~ spl0_235
| spl0_435 ),
inference(forward_demodulation,[],[f5516,f2312]) ).
fof(f5516,plain,
( ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation))))
| spl0_435 ),
inference(avatar_component_clause,[],[f5514]) ).
fof(f5525,plain,
( spl0_437
| ~ spl0_28
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f3413,f3310,f323,f5523]) ).
fof(f5523,plain,
( spl0_437
<=> ! [X0] : subclass(intersection(singleton_relation,X0),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f3413,plain,
( ! [X0] : subclass(intersection(singleton_relation,X0),subset_relation)
| ~ spl0_28
| ~ spl0_332 ),
inference(duplicate_literal_removal,[],[f3400]) ).
fof(f3400,plain,
( ! [X0] :
( subclass(intersection(singleton_relation,X0),subset_relation)
| subclass(intersection(singleton_relation,X0),subset_relation) )
| ~ spl0_28
| ~ spl0_332 ),
inference(resolution,[],[f3311,f324]) ).
fof(f5520,plain,
( ~ spl0_435
| spl0_436
| ~ spl0_106
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1201,f1163,f802,f5518,f5514]) ).
fof(f5518,plain,
( spl0_436
<=> ! [X0,X1] :
( ~ member(unordered_pair(X0,X1),element_relation)
| member(unordered_pair(X0,X1),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f1201,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(X0,X1),element_relation)
| member(unordered_pair(X0,X1),singleton_relation)
| ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_106
| ~ spl0_143 ),
inference(resolution,[],[f1164,f803]) ).
fof(f5512,plain,
( spl0_434
| ~ spl0_106
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1187,f1159,f802,f5510]) ).
fof(f5510,plain,
( spl0_434
<=> ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),null_class)
| ~ member(unordered_pair(X0,X1),X2)
| null_class = X2
| ~ subclass(universal_class,regular(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f1187,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),null_class)
| ~ member(unordered_pair(X0,X1),X2)
| null_class = X2
| ~ subclass(universal_class,regular(X2)) )
| ~ spl0_106
| ~ spl0_142 ),
inference(resolution,[],[f1160,f803]) ).
fof(f5508,plain,
( spl0_433
| ~ spl0_23
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1182,f1159,f299,f5506]) ).
fof(f5506,plain,
( spl0_433
<=> ! [X0] :
( member(regular(regular(X0)),null_class)
| ~ member(regular(regular(X0)),X0)
| null_class = X0
| null_class = regular(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f1182,plain,
( ! [X0] :
( member(regular(regular(X0)),null_class)
| ~ member(regular(regular(X0)),X0)
| null_class = X0
| null_class = regular(X0) )
| ~ spl0_23
| ~ spl0_142 ),
inference(resolution,[],[f1160,f300]) ).
fof(f5503,plain,
( ~ spl0_432
| ~ spl0_235
| spl0_431 ),
inference(avatar_split_clause,[],[f5498,f5494,f2310,f5500]) ).
fof(f5500,plain,
( spl0_432
<=> member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f5494,plain,
( spl0_431
<=> member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f5498,plain,
( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation)
| ~ spl0_235
| spl0_431 ),
inference(forward_demodulation,[],[f5496,f2312]) ).
fof(f5496,plain,
( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
| spl0_431 ),
inference(avatar_component_clause,[],[f5494]) ).
fof(f5497,plain,
( spl0_430
| ~ spl0_431
| ~ spl0_112
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1001,f959,f884,f5494,f5490]) ).
fof(f1001,plain,
( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
| null_class = complement(domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_112
| ~ spl0_125 ),
inference(resolution,[],[f960,f885]) ).
fof(f5487,plain,
( ~ spl0_429
| ~ spl0_235
| spl0_426 ),
inference(avatar_split_clause,[],[f5471,f5467,f2310,f5484]) ).
fof(f5484,plain,
( spl0_429
<=> member(regular(complement(complement(compose(element_relation,complement(singleton_relation))))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f5467,plain,
( spl0_426
<=> member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f5471,plain,
( ~ member(regular(complement(complement(compose(element_relation,complement(singleton_relation))))),singleton_relation)
| ~ spl0_235
| spl0_426 ),
inference(forward_demodulation,[],[f5469,f2312]) ).
fof(f5469,plain,
( ~ member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
| spl0_426 ),
inference(avatar_component_clause,[],[f5467]) ).
fof(f5482,plain,
( spl0_428
| ~ spl0_235
| ~ spl0_244
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f3386,f3210,f2364,f2310,f5479]) ).
fof(f3386,plain,
( subclass(singleton_relation,intersection(subset_relation,singleton_relation))
| ~ spl0_235
| ~ spl0_244
| ~ spl0_327 ),
inference(forward_demodulation,[],[f3371,f2312]) ).
fof(f3371,plain,
( subclass(identity_relation,intersection(subset_relation,identity_relation))
| ~ spl0_244
| ~ spl0_327 ),
inference(duplicate_literal_removal,[],[f3362]) ).
fof(f3362,plain,
( subclass(identity_relation,intersection(subset_relation,identity_relation))
| subclass(identity_relation,intersection(subset_relation,identity_relation))
| ~ spl0_244
| ~ spl0_327 ),
inference(resolution,[],[f3211,f2365]) ).
fof(f5477,plain,
( ~ spl0_427
| ~ spl0_235
| spl0_425 ),
inference(avatar_split_clause,[],[f5472,f5463,f2310,f5474]) ).
fof(f5474,plain,
( spl0_427
<=> null_class = complement(complement(compose(element_relation,complement(singleton_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f5472,plain,
( null_class != complement(complement(compose(element_relation,complement(singleton_relation))))
| ~ spl0_235
| spl0_425 ),
inference(forward_demodulation,[],[f5464,f2312]) ).
fof(f5464,plain,
( null_class != complement(complement(compose(element_relation,complement(identity_relation))))
| spl0_425 ),
inference(avatar_component_clause,[],[f5463]) ).
fof(f5470,plain,
( spl0_425
| ~ spl0_426
| ~ spl0_112
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f996,f955,f884,f5467,f5463]) ).
fof(f996,plain,
( ~ member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
| null_class = complement(complement(compose(element_relation,complement(identity_relation))))
| ~ spl0_112
| ~ spl0_124 ),
inference(resolution,[],[f956,f885]) ).
fof(f5461,plain,
( spl0_424
| ~ spl0_44
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f897,f884,f424,f5459]) ).
fof(f5459,plain,
( spl0_424
<=> ! [X0] :
( null_class = complement(complement(X0))
| member(regular(complement(complement(X0))),X0)
| ~ member(regular(complement(complement(X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f897,plain,
( ! [X0] :
( null_class = complement(complement(X0))
| member(regular(complement(complement(X0))),X0)
| ~ member(regular(complement(complement(X0))),universal_class) )
| ~ spl0_44
| ~ spl0_112 ),
inference(resolution,[],[f885,f425]) ).
fof(f5172,plain,
( spl0_423
| ~ spl0_27
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f3380,f3210,f319,f5170]) ).
fof(f3380,plain,
( ! [X0] : subclass(X0,intersection(X0,X0))
| ~ spl0_27
| ~ spl0_327 ),
inference(duplicate_literal_removal,[],[f3345]) ).
fof(f3345,plain,
( ! [X0] :
( subclass(X0,intersection(X0,X0))
| subclass(X0,intersection(X0,X0)) )
| ~ spl0_27
| ~ spl0_327 ),
inference(resolution,[],[f3211,f320]) ).
fof(f5145,plain,
( spl0_422
| ~ spl0_235
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f4810,f4807,f2310,f5143]) ).
fof(f5143,plain,
( spl0_422
<=> ! [X0,X1] :
( ~ subclass(singleton_relation,X0)
| ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X1,subset_relation)
| member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f4807,plain,
( spl0_411
<=> ! [X0,X1] :
( ~ subclass(identity_relation,X0)
| ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X1,subset_relation)
| member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f4810,plain,
( ! [X0,X1] :
( ~ subclass(singleton_relation,X0)
| ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X1,subset_relation)
| member(X1,X0) )
| ~ spl0_235
| ~ spl0_411 ),
inference(forward_demodulation,[],[f4808,f2312]) ).
fof(f4808,plain,
( ! [X0,X1] :
( ~ subclass(identity_relation,X0)
| ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X1,subset_relation)
| member(X1,X0) )
| ~ spl0_411 ),
inference(avatar_component_clause,[],[f4807]) ).
fof(f5141,plain,
( spl0_421
| ~ spl0_235
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f4801,f4798,f2310,f5139]) ).
fof(f5139,plain,
( spl0_421
<=> ! [X0,X1] :
( ~ member(X1,complement(compose(element_relation,complement(singleton_relation))))
| ~ subclass(singleton_relation,X0)
| ~ member(X1,element_relation)
| member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f4798,plain,
( spl0_409
<=> ! [X0,X1] :
( ~ subclass(singleton_relation,X0)
| ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X1,element_relation)
| member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f4801,plain,
( ! [X0,X1] :
( ~ member(X1,complement(compose(element_relation,complement(singleton_relation))))
| ~ subclass(singleton_relation,X0)
| ~ member(X1,element_relation)
| member(X1,X0) )
| ~ spl0_235
| ~ spl0_409 ),
inference(forward_demodulation,[],[f4799,f2312]) ).
fof(f4799,plain,
( ! [X0,X1] :
( ~ subclass(singleton_relation,X0)
| ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X1,element_relation)
| member(X1,X0) )
| ~ spl0_409 ),
inference(avatar_component_clause,[],[f4798]) ).
fof(f4856,plain,
( spl0_420
| ~ spl0_243
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f3375,f3210,f2360,f4853]) ).
fof(f3375,plain,
( subclass(singleton_relation,intersection(element_relation,singleton_relation))
| ~ spl0_243
| ~ spl0_327 ),
inference(duplicate_literal_removal,[],[f3351]) ).
fof(f3351,plain,
( subclass(singleton_relation,intersection(element_relation,singleton_relation))
| subclass(singleton_relation,intersection(element_relation,singleton_relation))
| ~ spl0_243
| ~ spl0_327 ),
inference(resolution,[],[f3211,f2361]) ).
fof(f4851,plain,
( spl0_419
| ~ spl0_235
| ~ spl0_403 ),
inference(avatar_split_clause,[],[f4776,f4773,f2310,f4849]) ).
fof(f4773,plain,
( spl0_403
<=> ! [X0] :
( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
| subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f4776,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation)
| subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_235
| ~ spl0_403 ),
inference(forward_demodulation,[],[f4774,f2312]) ).
fof(f4774,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
| subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_403 ),
inference(avatar_component_clause,[],[f4773]) ).
fof(f4847,plain,
( spl0_418
| ~ spl0_235
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f4771,f4767,f2310,f4845]) ).
fof(f4767,plain,
( spl0_402
<=> ! [X0] :
( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
| subclass(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f4771,plain,
( ! [X0] :
( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
| ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(singleton_relation)))),singleton_relation) )
| ~ spl0_235
| ~ spl0_402 ),
inference(forward_demodulation,[],[f4770,f2312]) ).
fof(f4770,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(singleton_relation)))),singleton_relation)
| subclass(X0,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_235
| ~ spl0_402 ),
inference(forward_demodulation,[],[f4768,f2312]) ).
fof(f4768,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
| subclass(X0,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_402 ),
inference(avatar_component_clause,[],[f4767]) ).
fof(f4834,plain,
( spl0_417
| ~ spl0_134
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1406,f1365,f1083,f4832]) ).
fof(f1406,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
| subclass(intersection(X0,X1),intersection(X2,X0)) )
| ~ spl0_134
| ~ spl0_164 ),
inference(duplicate_literal_removal,[],[f1387]) ).
fof(f1387,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
| subclass(intersection(X0,X1),intersection(X2,X0))
| subclass(intersection(X0,X1),intersection(X2,X0)) )
| ~ spl0_134
| ~ spl0_164 ),
inference(resolution,[],[f1366,f1084]) ).
fof(f4830,plain,
( spl0_416
| ~ spl0_135
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1405,f1365,f1087,f4828]) ).
fof(f1405,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
| subclass(intersection(X0,X1),intersection(X2,X1)) )
| ~ spl0_135
| ~ spl0_164 ),
inference(duplicate_literal_removal,[],[f1388]) ).
fof(f1388,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
| subclass(intersection(X0,X1),intersection(X2,X1))
| subclass(intersection(X0,X1),intersection(X2,X1)) )
| ~ spl0_135
| ~ spl0_164 ),
inference(resolution,[],[f1366,f1088]) ).
fof(f4826,plain,
( spl0_415
| ~ spl0_23
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1342,f1316,f299,f4824]) ).
fof(f4824,plain,
( spl0_415
<=> ! [X0,X1] :
( member(X1,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f1342,plain,
( ! [X0,X1] :
( member(X1,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_23
| ~ spl0_160 ),
inference(duplicate_literal_removal,[],[f1329]) ).
fof(f1329,plain,
( ! [X0,X1] :
( member(X1,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class )
| ~ spl0_23
| ~ spl0_160 ),
inference(superposition,[],[f300,f1317]) ).
fof(f4822,plain,
( spl0_414
| ~ spl0_23
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1337,f1316,f299,f4820]) ).
fof(f4820,plain,
( spl0_414
<=> ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f1337,plain,
( ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_23
| ~ spl0_160 ),
inference(duplicate_literal_removal,[],[f1334]) ).
fof(f1334,plain,
( ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class )
| ~ spl0_23
| ~ spl0_160 ),
inference(superposition,[],[f300,f1317]) ).
fof(f4818,plain,
( spl0_413
| ~ spl0_31
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1263,f1247,f335,f4816]) ).
fof(f4816,plain,
( spl0_413
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f1263,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X0) )
| ~ spl0_31
| ~ spl0_152 ),
inference(resolution,[],[f1248,f336]) ).
fof(f4814,plain,
( spl0_412
| ~ spl0_32
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1262,f1247,f339,f4812]) ).
fof(f4812,plain,
( spl0_412
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f1262,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X1) )
| ~ spl0_32
| ~ spl0_152 ),
inference(resolution,[],[f1248,f340]) ).
fof(f4809,plain,
( spl0_411
| ~ spl0_43
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1258,f1243,f393,f4807]) ).
fof(f1258,plain,
( ! [X0,X1] :
( ~ subclass(identity_relation,X0)
| ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X1,subset_relation)
| member(X1,X0) )
| ~ spl0_43
| ~ spl0_151 ),
inference(superposition,[],[f1244,f395]) ).
fof(f4805,plain,
( spl0_410
| ~ spl0_28
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f3344,f3193,f323,f4803]) ).
fof(f4803,plain,
( spl0_410
<=> ! [X0] : subclass(intersection(X0,singleton_relation),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f3344,plain,
( ! [X0] : subclass(intersection(X0,singleton_relation),element_relation)
| ~ spl0_28
| ~ spl0_324 ),
inference(duplicate_literal_removal,[],[f3335]) ).
fof(f3335,plain,
( ! [X0] :
( subclass(intersection(X0,singleton_relation),element_relation)
| subclass(intersection(X0,singleton_relation),element_relation) )
| ~ spl0_28
| ~ spl0_324 ),
inference(resolution,[],[f3194,f324]) ).
fof(f4800,plain,
( spl0_409
| ~ spl0_41
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1257,f1243,f384,f4798]) ).
fof(f1257,plain,
( ! [X0,X1] :
( ~ subclass(singleton_relation,X0)
| ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X1,element_relation)
| member(X1,X0) )
| ~ spl0_41
| ~ spl0_151 ),
inference(superposition,[],[f1244,f386]) ).
fof(f4796,plain,
( spl0_408
| ~ spl0_40
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1253,f1243,f380,f4794]) ).
fof(f4794,plain,
( spl0_408
<=> ! [X2,X0,X1] :
( ~ subclass(null_class,X1)
| ~ member(X2,X0)
| ~ member(X2,regular(X0))
| member(X2,X1)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f1253,plain,
( ! [X2,X0,X1] :
( ~ subclass(null_class,X1)
| ~ member(X2,X0)
| ~ member(X2,regular(X0))
| member(X2,X1)
| null_class = X0 )
| ~ spl0_40
| ~ spl0_151 ),
inference(superposition,[],[f1244,f381]) ).
fof(f4792,plain,
( spl0_407
| ~ spl0_31
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1134,f1087,f335,f4790]) ).
fof(f1134,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1) )
| ~ spl0_31
| ~ spl0_135 ),
inference(resolution,[],[f1088,f336]) ).
fof(f4788,plain,
( spl0_406
| ~ spl0_32
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1133,f1087,f339,f4786]) ).
fof(f1133,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2) )
| ~ spl0_32
| ~ spl0_135 ),
inference(resolution,[],[f1088,f340]) ).
fof(f4784,plain,
( spl0_405
| ~ spl0_31
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1116,f1083,f335,f4782]) ).
fof(f1116,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0) )
| ~ spl0_31
| ~ spl0_134 ),
inference(resolution,[],[f1084,f336]) ).
fof(f4780,plain,
( spl0_404
| ~ spl0_32
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1115,f1083,f339,f4778]) ).
fof(f1115,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1) )
| ~ spl0_32
| ~ spl0_134 ),
inference(resolution,[],[f1084,f340]) ).
fof(f4775,plain,
( spl0_403
| ~ spl0_28
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f998,f959,f323,f4773]) ).
fof(f998,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
| subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_28
| ~ spl0_125 ),
inference(resolution,[],[f960,f324]) ).
fof(f4769,plain,
( spl0_402
| ~ spl0_28
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f994,f955,f323,f4767]) ).
fof(f994,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
| subclass(X0,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_28
| ~ spl0_124 ),
inference(resolution,[],[f956,f324]) ).
fof(f4765,plain,
( spl0_401
| ~ spl0_48
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f973,f919,f444,f4763]) ).
fof(f4763,plain,
( spl0_401
<=> ! [X2,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| null_class = X0
| regular(X0) = X1
| regular(X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f973,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| null_class = X0
| regular(X0) = X1
| regular(X0) = X2 )
| ~ spl0_48
| ~ spl0_116 ),
inference(resolution,[],[f920,f445]) ).
fof(f4738,plain,
( spl0_400
| ~ spl0_28
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f3322,f3172,f323,f4736]) ).
fof(f4736,plain,
( spl0_400
<=> ! [X0] : subclass(intersection(singleton_relation,X0),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f3322,plain,
( ! [X0] : subclass(intersection(singleton_relation,X0),element_relation)
| ~ spl0_28
| ~ spl0_320 ),
inference(duplicate_literal_removal,[],[f3313]) ).
fof(f3313,plain,
( ! [X0] :
( subclass(intersection(singleton_relation,X0),element_relation)
| subclass(intersection(singleton_relation,X0),element_relation) )
| ~ spl0_28
| ~ spl0_320 ),
inference(resolution,[],[f3173,f324]) ).
fof(f4643,plain,
( spl0_399
| ~ spl0_235
| ~ spl0_392 ),
inference(avatar_split_clause,[],[f4246,f4243,f2310,f4641]) ).
fof(f4641,plain,
( spl0_399
<=> ! [X0] :
( member(X0,compose(element_relation,complement(singleton_relation)))
| ~ member(X0,element_relation)
| member(X0,singleton_relation)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f4243,plain,
( spl0_392
<=> ! [X0] :
( ~ member(X0,element_relation)
| member(X0,singleton_relation)
| member(X0,compose(element_relation,complement(identity_relation)))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f4246,plain,
( ! [X0] :
( member(X0,compose(element_relation,complement(singleton_relation)))
| ~ member(X0,element_relation)
| member(X0,singleton_relation)
| ~ member(X0,universal_class) )
| ~ spl0_235
| ~ spl0_392 ),
inference(forward_demodulation,[],[f4244,f2312]) ).
fof(f4244,plain,
( ! [X0] :
( ~ member(X0,element_relation)
| member(X0,singleton_relation)
| member(X0,compose(element_relation,complement(identity_relation)))
| ~ member(X0,universal_class) )
| ~ spl0_392 ),
inference(avatar_component_clause,[],[f4243]) ).
fof(f4367,plain,
( spl0_398
| ~ spl0_235
| ~ spl0_244
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3237,f3137,f2364,f2310,f4364]) ).
fof(f3237,plain,
( subclass(singleton_relation,cross_product(universal_class,universal_class))
| ~ spl0_235
| ~ spl0_244
| ~ spl0_313 ),
inference(forward_demodulation,[],[f3236,f2312]) ).
fof(f3236,plain,
( subclass(identity_relation,cross_product(universal_class,universal_class))
| ~ spl0_244
| ~ spl0_313 ),
inference(duplicate_literal_removal,[],[f3225]) ).
fof(f3225,plain,
( subclass(identity_relation,cross_product(universal_class,universal_class))
| subclass(identity_relation,cross_product(universal_class,universal_class))
| ~ spl0_244
| ~ spl0_313 ),
inference(resolution,[],[f3138,f2365]) ).
fof(f4272,plain,
( spl0_397
| ~ spl0_130
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1404,f1365,f1012,f4270]) ).
fof(f1404,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2))
| ~ subclass(X0,X2) )
| ~ spl0_130
| ~ spl0_164 ),
inference(duplicate_literal_removal,[],[f1389]) ).
fof(f1389,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2))
| ~ subclass(X0,X2)
| subclass(X0,intersection(X1,X2)) )
| ~ spl0_130
| ~ spl0_164 ),
inference(resolution,[],[f1366,f1013]) ).
fof(f4268,plain,
( ~ spl0_395
| spl0_396
| ~ spl0_12
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1310,f1294,f254,f4265,f4261]) ).
fof(f4261,plain,
( spl0_395
<=> inductive(domain_of(regular(cross_product(unordered_pair(null_class,null_class),universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f4265,plain,
( spl0_396
<=> null_class = cross_product(unordered_pair(null_class,null_class),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f1310,plain,
( null_class = cross_product(unordered_pair(null_class,null_class),universal_class)
| ~ inductive(domain_of(regular(cross_product(unordered_pair(null_class,null_class),universal_class))))
| ~ spl0_12
| ~ spl0_158 ),
inference(resolution,[],[f1295,f255]) ).
fof(f4259,plain,
( spl0_394
| ~ spl0_20
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1264,f1247,f287,f4257]) ).
fof(f4257,plain,
( spl0_394
<=> ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f1264,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0) )
| ~ spl0_20
| ~ spl0_152 ),
inference(resolution,[],[f1248,f288]) ).
fof(f4251,plain,
( spl0_182
| ~ spl0_6
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f2511,f2479,f228,f1538]) ).
fof(f2479,plain,
( spl0_265
<=> ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f2511,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ spl0_6
| ~ spl0_265 ),
inference(resolution,[],[f2480,f229]) ).
fof(f2480,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(null_class,X0) )
| ~ spl0_265 ),
inference(avatar_component_clause,[],[f2479]) ).
fof(f4250,plain,
( spl0_393
| ~ spl0_22
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1252,f1243,f295,f4248]) ).
fof(f4248,plain,
( spl0_393
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,cross_product(universal_class,universal_class))
| ~ function(intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f1252,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,cross_product(universal_class,universal_class))
| ~ function(intersection(X1,X2)) )
| ~ spl0_22
| ~ spl0_151 ),
inference(resolution,[],[f1244,f296]) ).
fof(f4245,plain,
( spl0_392
| ~ spl0_44
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1191,f1163,f424,f4243]) ).
fof(f1191,plain,
( ! [X0] :
( ~ member(X0,element_relation)
| member(X0,singleton_relation)
| member(X0,compose(element_relation,complement(identity_relation)))
| ~ member(X0,universal_class) )
| ~ spl0_44
| ~ spl0_143 ),
inference(resolution,[],[f1164,f425]) ).
fof(f4241,plain,
( spl0_391
| ~ spl0_113
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1136,f1087,f888,f4239]) ).
fof(f1136,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,null_class),X1)
| member(not_subclass_element(intersection(X0,null_class),X1),X2)
| null_class = X2 )
| ~ spl0_113
| ~ spl0_135 ),
inference(resolution,[],[f1088,f889]) ).
fof(f4237,plain,
( spl0_390
| ~ spl0_38
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1130,f1087,f372,f4235]) ).
fof(f1130,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,X1),X2)
| ~ subclass(X1,X3)
| member(not_subclass_element(intersection(X0,X1),X2),X3) )
| ~ spl0_38
| ~ spl0_135 ),
inference(resolution,[],[f1088,f373]) ).
fof(f4233,plain,
( spl0_389
| ~ spl0_113
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1118,f1083,f888,f4231]) ).
fof(f1118,plain,
( ! [X2,X0,X1] :
( subclass(intersection(null_class,X0),X1)
| member(not_subclass_element(intersection(null_class,X0),X1),X2)
| null_class = X2 )
| ~ spl0_113
| ~ spl0_134 ),
inference(resolution,[],[f1084,f889]) ).
fof(f4229,plain,
( spl0_388
| ~ spl0_38
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1112,f1083,f372,f4227]) ).
fof(f1112,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,X1),X2)
| ~ subclass(X0,X3)
| member(not_subclass_element(intersection(X0,X1),X2),X3) )
| ~ spl0_38
| ~ spl0_134 ),
inference(resolution,[],[f1084,f373]) ).
fof(f4225,plain,
( spl0_387
| ~ spl0_31
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1047,f1008,f335,f4223]) ).
fof(f1047,plain,
( ! [X2,X0,X1] :
( null_class = intersection(X0,intersection(X1,X2))
| member(regular(intersection(X0,intersection(X1,X2))),X1) )
| ~ spl0_31
| ~ spl0_129 ),
inference(resolution,[],[f1009,f336]) ).
fof(f4221,plain,
( spl0_386
| ~ spl0_32
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1046,f1008,f339,f4219]) ).
fof(f1046,plain,
( ! [X2,X0,X1] :
( null_class = intersection(X0,intersection(X1,X2))
| member(regular(intersection(X0,intersection(X1,X2))),X2) )
| ~ spl0_32
| ~ spl0_129 ),
inference(resolution,[],[f1009,f340]) ).
fof(f4217,plain,
( spl0_385
| ~ spl0_31
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1031,f1004,f335,f4215]) ).
fof(f1031,plain,
( ! [X2,X0,X1] :
( null_class = intersection(intersection(X0,X1),X2)
| member(regular(intersection(intersection(X0,X1),X2)),X0) )
| ~ spl0_31
| ~ spl0_128 ),
inference(resolution,[],[f1005,f336]) ).
fof(f4213,plain,
( spl0_384
| ~ spl0_32
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1030,f1004,f339,f4211]) ).
fof(f1030,plain,
( ! [X2,X0,X1] :
( null_class = intersection(intersection(X0,X1),X2)
| member(regular(intersection(intersection(X0,X1),X2)),X1) )
| ~ spl0_32
| ~ spl0_128 ),
inference(resolution,[],[f1005,f340]) ).
fof(f4209,plain,
( spl0_383
| ~ spl0_76
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2238,f2223,f608,f4206]) ).
fof(f2238,plain,
( subclass(subset_relation,cross_product(universal_class,universal_class))
| ~ spl0_76
| ~ spl0_223 ),
inference(superposition,[],[f2224,f610]) ).
fof(f4204,plain,
( spl0_382
| ~ spl0_115
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f990,f951,f915,f4202]) ).
fof(f4202,plain,
( spl0_382
<=> ! [X0,X1] :
( ~ member(not_subclass_element(complement(regular(X0)),X1),null_class)
| null_class = X0
| subclass(complement(regular(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f990,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(complement(regular(X0)),X1),null_class)
| null_class = X0
| subclass(complement(regular(X0)),X1) )
| ~ spl0_115
| ~ spl0_123 ),
inference(resolution,[],[f952,f916]) ).
fof(f4200,plain,
( spl0_381
| ~ spl0_48
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f846,f802,f444,f4198]) ).
fof(f4198,plain,
( spl0_381
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| unordered_pair(X2,X3) = X0
| unordered_pair(X2,X3) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f846,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| unordered_pair(X2,X3) = X0
| unordered_pair(X2,X3) = X1 )
| ~ spl0_48
| ~ spl0_106 ),
inference(resolution,[],[f803,f445]) ).
fof(f3836,plain,
( spl0_380
| ~ spl0_106
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1737,f1711,f802,f3834]) ).
fof(f3834,plain,
( spl0_380
<=> ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),X2)
| ~ subclass(universal_class,X2)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f1737,plain,
( ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),X2)
| ~ subclass(universal_class,X2)
| cross_product(X0,X1) = null_class )
| ~ spl0_106
| ~ spl0_198 ),
inference(superposition,[],[f803,f1712]) ).
fof(f3832,plain,
( spl0_379
| ~ spl0_32
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1354,f1351,f339,f3830]) ).
fof(f3830,plain,
( spl0_379
<=> ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f1354,plain,
( ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) )
| ~ spl0_32
| ~ spl0_162 ),
inference(resolution,[],[f1352,f340]) ).
fof(f3828,plain,
( spl0_378
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1336,f1316,f3826]) ).
fof(f3826,plain,
( spl0_378
<=> ! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f1336,plain,
( ! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class )
| ~ spl0_160 ),
inference(equality_factoring,[],[f1317]) ).
fof(f3824,plain,
( spl0_377
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1335,f1316,f3822]) ).
fof(f3822,plain,
( spl0_377
<=> ! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f1335,plain,
( ! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class )
| ~ spl0_160 ),
inference(equality_factoring,[],[f1317]) ).
fof(f3820,plain,
( spl0_376
| ~ spl0_134
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1307,f1290,f1083,f3818]) ).
fof(f1290,plain,
( spl0_157
<=> ! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| ~ member(not_subclass_element(X0,complement(X1)),universal_class)
| subclass(X0,complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1307,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
| subclass(intersection(universal_class,X0),complement(X1)) )
| ~ spl0_134
| ~ spl0_157 ),
inference(duplicate_literal_removal,[],[f1302]) ).
fof(f1302,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
| subclass(intersection(universal_class,X0),complement(X1))
| subclass(intersection(universal_class,X0),complement(X1)) )
| ~ spl0_134
| ~ spl0_157 ),
inference(resolution,[],[f1291,f1084]) ).
fof(f1291,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,complement(X1)),universal_class)
| member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1)) )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f1290]) ).
fof(f3816,plain,
( spl0_375
| ~ spl0_135
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1306,f1290,f1087,f3814]) ).
fof(f1306,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
| subclass(intersection(X0,universal_class),complement(X1)) )
| ~ spl0_135
| ~ spl0_157 ),
inference(duplicate_literal_removal,[],[f1303]) ).
fof(f1303,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
| subclass(intersection(X0,universal_class),complement(X1))
| subclass(intersection(X0,universal_class),complement(X1)) )
| ~ spl0_135
| ~ spl0_157 ),
inference(resolution,[],[f1291,f1088]) ).
fof(f3812,plain,
( spl0_374
| ~ spl0_22
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1176,f1155,f295,f3810]) ).
fof(f3810,plain,
( spl0_374
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,X1)
| member(X0,cross_product(universal_class,universal_class))
| ~ function(complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f1155,plain,
( spl0_141
<=> ! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,universal_class)
| ~ subclass(complement(X1),X2)
| member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1176,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,X1)
| member(X0,cross_product(universal_class,universal_class))
| ~ function(complement(X1)) )
| ~ spl0_22
| ~ spl0_141 ),
inference(resolution,[],[f1156,f296]) ).
fof(f1156,plain,
( ! [X2,X0,X1] :
( ~ subclass(complement(X1),X2)
| ~ member(X0,universal_class)
| member(X0,X1)
| member(X0,X2) )
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1155]) ).
fof(f3808,plain,
( spl0_373
| ~ spl0_20
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1135,f1087,f287,f3806]) ).
fof(f1135,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,complement(X1)),X2)
| ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1) )
| ~ spl0_20
| ~ spl0_135 ),
inference(resolution,[],[f1088,f288]) ).
fof(f3804,plain,
( spl0_372
| ~ spl0_20
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1117,f1083,f287,f3802]) ).
fof(f1117,plain,
( ! [X2,X0,X1] :
( subclass(intersection(complement(X0),X1),X2)
| ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) )
| ~ spl0_20
| ~ spl0_134 ),
inference(resolution,[],[f1084,f288]) ).
fof(f3800,plain,
( ~ spl0_370
| spl0_371
| ~ spl0_114
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f3158,f2727,f892,f3797,f3793]) ).
fof(f3793,plain,
( spl0_370
<=> single_valued_class(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f3797,plain,
( spl0_371
<=> function(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f3158,plain,
( function(null_class)
| ~ single_valued_class(null_class)
| ~ spl0_114
| ~ spl0_284 ),
inference(resolution,[],[f2728,f893]) ).
fof(f3791,plain,
( spl0_369
| ~ spl0_113
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1067,f1012,f888,f3789]) ).
fof(f3789,plain,
( spl0_369
<=> ! [X2,X0,X1] :
( ~ subclass(X0,null_class)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),X2)
| null_class = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f1067,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,null_class)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),X2)
| null_class = X2 )
| ~ spl0_113
| ~ spl0_130 ),
inference(resolution,[],[f1013,f889]) ).
fof(f3787,plain,
( spl0_368
| ~ spl0_38
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1061,f1012,f372,f3785]) ).
fof(f3785,plain,
( spl0_368
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,X1)
| subclass(X0,X2)
| ~ subclass(X1,X3)
| member(not_subclass_element(X0,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f1061,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,X1)
| subclass(X0,X2)
| ~ subclass(X1,X3)
| member(not_subclass_element(X0,X2),X3) )
| ~ spl0_38
| ~ spl0_130 ),
inference(resolution,[],[f1013,f373]) ).
fof(f3783,plain,
( spl0_367
| ~ spl0_113
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1049,f1008,f888,f3781]) ).
fof(f3781,plain,
( spl0_367
<=> ! [X0,X1] :
( null_class = intersection(X0,null_class)
| member(regular(intersection(X0,null_class)),X1)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f1049,plain,
( ! [X0,X1] :
( null_class = intersection(X0,null_class)
| member(regular(intersection(X0,null_class)),X1)
| null_class = X1 )
| ~ spl0_113
| ~ spl0_129 ),
inference(resolution,[],[f1009,f889]) ).
fof(f3779,plain,
( spl0_366
| ~ spl0_38
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1043,f1008,f372,f3777]) ).
fof(f1043,plain,
( ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| ~ subclass(X1,X2)
| member(regular(intersection(X0,X1)),X2) )
| ~ spl0_38
| ~ spl0_129 ),
inference(resolution,[],[f1009,f373]) ).
fof(f3775,plain,
( spl0_365
| ~ spl0_113
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1033,f1004,f888,f3773]) ).
fof(f3773,plain,
( spl0_365
<=> ! [X0,X1] :
( null_class = intersection(null_class,X0)
| member(regular(intersection(null_class,X0)),X1)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f1033,plain,
( ! [X0,X1] :
( null_class = intersection(null_class,X0)
| member(regular(intersection(null_class,X0)),X1)
| null_class = X1 )
| ~ spl0_113
| ~ spl0_128 ),
inference(resolution,[],[f1005,f889]) ).
fof(f3771,plain,
( spl0_364
| ~ spl0_38
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1027,f1004,f372,f3769]) ).
fof(f1027,plain,
( ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| ~ subclass(X0,X2)
| member(regular(intersection(X0,X1)),X2) )
| ~ spl0_38
| ~ spl0_128 ),
inference(resolution,[],[f1005,f373]) ).
fof(f3767,plain,
( spl0_363
| ~ spl0_112
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f991,f951,f884,f3765]) ).
fof(f3765,plain,
( spl0_363
<=> ! [X0] :
( ~ member(regular(complement(regular(X0))),null_class)
| null_class = X0
| null_class = complement(regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f991,plain,
( ! [X0] :
( ~ member(regular(complement(regular(X0))),null_class)
| null_class = X0
| null_class = complement(regular(X0)) )
| ~ spl0_112
| ~ spl0_123 ),
inference(resolution,[],[f952,f885]) ).
fof(f3763,plain,
( spl0_362
| ~ spl0_111
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f966,f915,f823,f3761]) ).
fof(f3761,plain,
( spl0_362
<=> ! [X0] :
( subclass(complement(cross_product(universal_class,universal_class)),X0)
| ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f966,plain,
( ! [X0] :
( subclass(complement(cross_product(universal_class,universal_class)),X0)
| ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),subset_relation) )
| ~ spl0_111
| ~ spl0_115 ),
inference(resolution,[],[f916,f824]) ).
fof(f3759,plain,
( spl0_361
| ~ spl0_67
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f880,f823,f556,f3757]) ).
fof(f880,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(X1,universal_class) )
| ~ spl0_67
| ~ spl0_111 ),
inference(resolution,[],[f824,f557]) ).
fof(f3755,plain,
( spl0_360
| ~ spl0_68
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f879,f823,f560,f3753]) ).
fof(f879,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(X0,universal_class) )
| ~ spl0_68
| ~ spl0_111 ),
inference(resolution,[],[f824,f561]) ).
fof(f3747,plain,
( spl0_359
| ~ spl0_57
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f858,f815,f503,f3745]) ).
fof(f3745,plain,
( spl0_359
<=> ! [X0] :
( member(null_class,domain_of(domain_of(X0)))
| ~ inductive(domain_of(domain_of(flip(cross_product(X0,universal_class)))))
| ~ operation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f858,plain,
( ! [X0] :
( member(null_class,domain_of(domain_of(X0)))
| ~ inductive(domain_of(domain_of(flip(cross_product(X0,universal_class)))))
| ~ operation(X0) )
| ~ spl0_57
| ~ spl0_109 ),
inference(resolution,[],[f816,f504]) ).
fof(f3616,plain,
( spl0_358
| ~ spl0_235
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f3518,f3515,f2310,f3614]) ).
fof(f3515,plain,
( spl0_349
<=> ! [X0,X1] :
( ~ member(X0,identity_relation)
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
| member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f3518,plain,
( ! [X0,X1] :
( ~ member(X0,singleton_relation)
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
| member(X0,X1) )
| ~ spl0_235
| ~ spl0_349 ),
inference(forward_demodulation,[],[f3516,f2312]) ).
fof(f3516,plain,
( ! [X0,X1] :
( ~ member(X0,identity_relation)
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
| member(X0,X1) )
| ~ spl0_349 ),
inference(avatar_component_clause,[],[f3515]) ).
fof(f3597,plain,
( spl0_357
| ~ spl0_235
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f3513,f3510,f2310,f3595]) ).
fof(f3510,plain,
( spl0_348
<=> ! [X0,X1] :
( ~ member(X0,singleton_relation)
| ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
| member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f3513,plain,
( ! [X0,X1] :
( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X1)
| ~ member(X0,singleton_relation)
| member(X0,X1) )
| ~ spl0_235
| ~ spl0_348 ),
inference(forward_demodulation,[],[f3511,f2312]) ).
fof(f3511,plain,
( ! [X0,X1] :
( ~ member(X0,singleton_relation)
| ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
| member(X0,X1) )
| ~ spl0_348 ),
inference(avatar_component_clause,[],[f3510]) ).
fof(f3547,plain,
( spl0_356
| ~ spl0_72
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1416,f1369,f584,f3545]) ).
fof(f3545,plain,
( spl0_356
<=> ! [X0,X1] :
( ~ subclass(domain_relation,compose_class(X0))
| ~ member(X1,universal_class)
| compose(X0,X1) = domain_of(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f1416,plain,
( ! [X0,X1] :
( ~ subclass(domain_relation,compose_class(X0))
| ~ member(X1,universal_class)
| compose(X0,X1) = domain_of(X1) )
| ~ spl0_72
| ~ spl0_165 ),
inference(resolution,[],[f1370,f585]) ).
fof(f3543,plain,
( spl0_355
| ~ spl0_130
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1305,f1290,f1012,f3541]) ).
fof(f3541,plain,
( spl0_355
<=> ! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f1305,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class) )
| ~ spl0_130
| ~ spl0_157 ),
inference(duplicate_literal_removal,[],[f1304]) ).
fof(f1304,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class)
| subclass(X0,complement(X1)) )
| ~ spl0_130
| ~ spl0_157 ),
inference(resolution,[],[f1291,f1013]) ).
fof(f3539,plain,
( spl0_354
| ~ spl0_31
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1065,f1012,f335,f3537]) ).
fof(f3537,plain,
( spl0_354
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(not_subclass_element(X0,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f1065,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(not_subclass_element(X0,X3),X1) )
| ~ spl0_31
| ~ spl0_130 ),
inference(resolution,[],[f1013,f336]) ).
fof(f3535,plain,
( spl0_353
| ~ spl0_32
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1064,f1012,f339,f3533]) ).
fof(f3533,plain,
( spl0_353
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(not_subclass_element(X0,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f1064,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(not_subclass_element(X0,X3),X2) )
| ~ spl0_32
| ~ spl0_130 ),
inference(resolution,[],[f1013,f340]) ).
fof(f3531,plain,
( spl0_352
| ~ spl0_20
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1048,f1008,f287,f3529]) ).
fof(f1048,plain,
( ! [X0,X1] :
( null_class = intersection(X0,complement(X1))
| ~ member(regular(intersection(X0,complement(X1))),X1) )
| ~ spl0_20
| ~ spl0_129 ),
inference(resolution,[],[f1009,f288]) ).
fof(f3527,plain,
( spl0_351
| ~ spl0_20
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1032,f1004,f287,f3525]) ).
fof(f1032,plain,
( ! [X0,X1] :
( null_class = intersection(complement(X0),X1)
| ~ member(regular(intersection(complement(X0),X1)),X0) )
| ~ spl0_20
| ~ spl0_128 ),
inference(resolution,[],[f1005,f288]) ).
fof(f3523,plain,
( spl0_350
| ~ spl0_234
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2876,f2310,f2304,f3520]) ).
fof(f2876,plain,
( member(regular(singleton_relation),subset_relation)
| ~ spl0_234
| ~ spl0_235 ),
inference(superposition,[],[f2306,f2312]) ).
fof(f3517,plain,
( spl0_349
| ~ spl0_38
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f997,f959,f372,f3515]) ).
fof(f997,plain,
( ! [X0,X1] :
( ~ member(X0,identity_relation)
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
| member(X0,X1) )
| ~ spl0_38
| ~ spl0_125 ),
inference(resolution,[],[f960,f373]) ).
fof(f3512,plain,
( spl0_348
| ~ spl0_38
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f993,f955,f372,f3510]) ).
fof(f993,plain,
( ! [X0,X1] :
( ~ member(X0,singleton_relation)
| ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
| member(X0,X1) )
| ~ spl0_38
| ~ spl0_124 ),
inference(resolution,[],[f956,f373]) ).
fof(f3508,plain,
( spl0_347
| ~ spl0_28
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f989,f951,f323,f3506]) ).
fof(f989,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,regular(X1)),null_class)
| null_class = X1
| subclass(X0,regular(X1)) )
| ~ spl0_28
| ~ spl0_123 ),
inference(resolution,[],[f952,f324]) ).
fof(f3504,plain,
( spl0_346
| ~ spl0_38
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f988,f951,f372,f3502]) ).
fof(f3502,plain,
( spl0_346
<=> ! [X2,X0,X1] :
( ~ member(X0,null_class)
| null_class = X1
| ~ subclass(regular(X1),X2)
| member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f988,plain,
( ! [X2,X0,X1] :
( ~ member(X0,null_class)
| null_class = X1
| ~ subclass(regular(X1),X2)
| member(X0,X2) )
| ~ spl0_38
| ~ spl0_123 ),
inference(resolution,[],[f952,f373]) ).
fof(f3500,plain,
( spl0_345
| ~ spl0_38
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f972,f919,f372,f3498]) ).
fof(f972,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| null_class = X0
| ~ subclass(X1,X2)
| member(regular(X0),X2) )
| ~ spl0_38
| ~ spl0_116 ),
inference(resolution,[],[f920,f373]) ).
fof(f3493,plain,
( ~ spl0_343
| spl0_344
| ~ spl0_111
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f895,f884,f823,f3490,f3486]) ).
fof(f3486,plain,
( spl0_343
<=> member(regular(complement(cross_product(universal_class,universal_class))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f895,plain,
( null_class = complement(cross_product(universal_class,universal_class))
| ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation)
| ~ spl0_111
| ~ spl0_112 ),
inference(resolution,[],[f885,f824]) ).
fof(f3484,plain,
( spl0_342
| spl0_339
| ~ spl0_51
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f866,f815,f456,f3465,f3482]) ).
fof(f3482,plain,
( spl0_342
<=> ! [X0] :
( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| ~ single_valued_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f3465,plain,
( spl0_339
<=> member(null_class,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f456,plain,
( spl0_51
<=> ! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f866,plain,
( ! [X0] :
( member(null_class,identity_relation)
| ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| ~ single_valued_class(X0) )
| ~ spl0_51
| ~ spl0_109 ),
inference(resolution,[],[f816,f457]) ).
fof(f457,plain,
( ! [X0] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ single_valued_class(X0) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f456]) ).
fof(f3480,plain,
( spl0_341
| ~ spl0_4
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f2484,f2452,f219,f3477]) ).
fof(f2484,plain,
( null_class = complement(universal_class)
| ~ spl0_4
| ~ spl0_262 ),
inference(resolution,[],[f2453,f220]) ).
fof(f3474,plain,
( ~ spl0_340
| ~ spl0_235
| spl0_339 ),
inference(avatar_split_clause,[],[f3469,f3465,f2310,f3471]) ).
fof(f3471,plain,
( spl0_340
<=> member(null_class,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f3469,plain,
( ~ member(null_class,singleton_relation)
| ~ spl0_235
| spl0_339 ),
inference(forward_demodulation,[],[f3466,f2312]) ).
fof(f3466,plain,
( ~ member(null_class,identity_relation)
| spl0_339 ),
inference(avatar_component_clause,[],[f3465]) ).
fof(f3468,plain,
( spl0_338
| spl0_339
| ~ spl0_52
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f865,f815,f460,f3465,f3462]) ).
fof(f3462,plain,
( spl0_338
<=> ! [X0] :
( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f460,plain,
( spl0_52
<=> ! [X8] :
( ~ function(X8)
| subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f865,plain,
( ! [X0] :
( member(null_class,identity_relation)
| ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| ~ function(X0) )
| ~ spl0_52
| ~ spl0_109 ),
inference(resolution,[],[f816,f461]) ).
fof(f461,plain,
( ! [X8] :
( subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
| ~ function(X8) )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f3460,plain,
( spl0_336
| ~ spl0_337
| ~ spl0_78
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f831,f802,f624,f3457,f3454]) ).
fof(f3454,plain,
( spl0_336
<=> ! [X0,X1] : complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f3457,plain,
( spl0_337
<=> subclass(universal_class,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f831,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,successor_relation)
| complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 )
| ~ spl0_78
| ~ spl0_106 ),
inference(resolution,[],[f803,f625]) ).
fof(f3334,plain,
( spl0_335
| ~ spl0_235
| ~ spl0_323 ),
inference(avatar_split_clause,[],[f3191,f3187,f2310,f3332]) ).
fof(f3187,plain,
( spl0_323
<=> ! [X0,X1] :
( subclass(intersection(X0,identity_relation),X1)
| member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f3191,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(X0,singleton_relation),X1),subset_relation)
| subclass(intersection(X0,singleton_relation),X1) )
| ~ spl0_235
| ~ spl0_323 ),
inference(forward_demodulation,[],[f3190,f2312]) ).
fof(f3190,plain,
( ! [X0,X1] :
( subclass(intersection(X0,singleton_relation),X1)
| member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
| ~ spl0_235
| ~ spl0_323 ),
inference(forward_demodulation,[],[f3188,f2312]) ).
fof(f3188,plain,
( ! [X0,X1] :
( subclass(intersection(X0,identity_relation),X1)
| member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
| ~ spl0_323 ),
inference(avatar_component_clause,[],[f3187]) ).
fof(f3330,plain,
( spl0_334
| ~ spl0_235
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f3185,f3181,f2310,f3328]) ).
fof(f3181,plain,
( spl0_322
<=> ! [X0] :
( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(identity_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f3185,plain,
( ! [X0] :
( subclass(singleton_relation,X0)
| member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_235
| ~ spl0_322 ),
inference(forward_demodulation,[],[f3184,f2312]) ).
fof(f3184,plain,
( ! [X0] :
( member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(identity_relation,X0) )
| ~ spl0_235
| ~ spl0_322 ),
inference(forward_demodulation,[],[f3182,f2312]) ).
fof(f3182,plain,
( ! [X0] :
( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(identity_relation,X0) )
| ~ spl0_322 ),
inference(avatar_component_clause,[],[f3181]) ).
fof(f3326,plain,
( spl0_333
| ~ spl0_235
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f3179,f3176,f2310,f3324]) ).
fof(f3176,plain,
( spl0_321
<=> ! [X0] :
( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
| subclass(singleton_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f3179,plain,
( ! [X0] :
( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
| subclass(singleton_relation,X0) )
| ~ spl0_235
| ~ spl0_321 ),
inference(forward_demodulation,[],[f3177,f2312]) ).
fof(f3177,plain,
( ! [X0] :
( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
| subclass(singleton_relation,X0) )
| ~ spl0_321 ),
inference(avatar_component_clause,[],[f3176]) ).
fof(f3312,plain,
( spl0_332
| ~ spl0_235
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f3170,f3166,f2310,f3310]) ).
fof(f3166,plain,
( spl0_319
<=> ! [X0,X1] :
( subclass(intersection(identity_relation,X0),X1)
| member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f3170,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(singleton_relation,X0),X1),subset_relation)
| subclass(intersection(singleton_relation,X0),X1) )
| ~ spl0_235
| ~ spl0_319 ),
inference(forward_demodulation,[],[f3169,f2312]) ).
fof(f3169,plain,
( ! [X0,X1] :
( subclass(intersection(singleton_relation,X0),X1)
| member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
| ~ spl0_235
| ~ spl0_319 ),
inference(forward_demodulation,[],[f3167,f2312]) ).
fof(f3167,plain,
( ! [X0,X1] :
( subclass(intersection(identity_relation,X0),X1)
| member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
| ~ spl0_319 ),
inference(avatar_component_clause,[],[f3166]) ).
fof(f3308,plain,
( spl0_331
| ~ spl0_235
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2880,f2466,f2310,f3305]) ).
fof(f3305,plain,
( spl0_331
<=> subclass(singleton_relation,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f2880,plain,
( subclass(singleton_relation,subset_relation)
| ~ spl0_235
| ~ spl0_264 ),
inference(superposition,[],[f2468,f2312]) ).
fof(f3224,plain,
( spl0_330
| ~ spl0_6
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1442,f1377,f228,f3222]) ).
fof(f3222,plain,
( spl0_330
<=> ! [X0] :
( ~ function(domain_of(X0))
| compatible(domain_of(X0),X0,flip(cross_product(domain_of(X0),universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f1377,plain,
( spl0_167
<=> ! [X0,X1] :
( compatible(domain_of(X0),X0,X1)
| ~ function(domain_of(X0))
| ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1442,plain,
( ! [X0] :
( ~ function(domain_of(X0))
| compatible(domain_of(X0),X0,flip(cross_product(domain_of(X0),universal_class))) )
| ~ spl0_6
| ~ spl0_167 ),
inference(resolution,[],[f1378,f229]) ).
fof(f1378,plain,
( ! [X0,X1] :
( ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1)))
| ~ function(domain_of(X0))
| compatible(domain_of(X0),X0,X1) )
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f1377]) ).
fof(f3220,plain,
( spl0_329
| ~ spl0_57
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1441,f1377,f503,f3218]) ).
fof(f3218,plain,
( spl0_329
<=> ! [X0] :
( ~ function(domain_of(X0))
| compatible(domain_of(X0),X0,domain_of(X0))
| ~ operation(domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f1441,plain,
( ! [X0] :
( ~ function(domain_of(X0))
| compatible(domain_of(X0),X0,domain_of(X0))
| ~ operation(domain_of(X0)) )
| ~ spl0_57
| ~ spl0_167 ),
inference(resolution,[],[f1378,f504]) ).
fof(f3216,plain,
( spl0_328
| ~ spl0_67
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1410,f1369,f556,f3214]) ).
fof(f1410,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(X2),X1) )
| ~ spl0_67
| ~ spl0_165 ),
inference(resolution,[],[f1370,f557]) ).
fof(f3212,plain,
( spl0_327
| ~ spl0_27
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1407,f1365,f319,f3210]) ).
fof(f1407,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0)) )
| ~ spl0_27
| ~ spl0_164 ),
inference(duplicate_literal_removal,[],[f1386]) ).
fof(f1386,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0))
| subclass(X0,intersection(X1,X0)) )
| ~ spl0_27
| ~ spl0_164 ),
inference(resolution,[],[f1366,f320]) ).
fof(f3203,plain,
( spl0_325
| spl0_326
| ~ spl0_12
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1180,f1159,f254,f3200,f3197]) ).
fof(f3197,plain,
( spl0_325
<=> ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(regular(X0))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f3200,plain,
( spl0_326
<=> member(null_class,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f1180,plain,
( ! [X0] :
( member(null_class,null_class)
| ~ member(null_class,X0)
| null_class = X0
| ~ inductive(regular(X0)) )
| ~ spl0_12
| ~ spl0_142 ),
inference(resolution,[],[f1160,f255]) ).
fof(f3195,plain,
( spl0_324
| ~ spl0_97
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1139,f1087,f731,f3193]) ).
fof(f1139,plain,
( ! [X0,X1] :
( subclass(intersection(X0,singleton_relation),X1)
| member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation) )
| ~ spl0_97
| ~ spl0_135 ),
inference(resolution,[],[f1088,f732]) ).
fof(f3189,plain,
( spl0_323
| ~ spl0_103
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1138,f1087,f761,f3187]) ).
fof(f1138,plain,
( ! [X0,X1] :
( subclass(intersection(X0,identity_relation),X1)
| member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
| ~ spl0_103
| ~ spl0_135 ),
inference(resolution,[],[f1088,f762]) ).
fof(f3183,plain,
( spl0_322
| ~ spl0_43
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1127,f1083,f393,f3181]) ).
fof(f1127,plain,
( ! [X0] :
( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(identity_relation,X0) )
| ~ spl0_43
| ~ spl0_134 ),
inference(superposition,[],[f1084,f395]) ).
fof(f3178,plain,
( spl0_321
| ~ spl0_41
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1126,f1083,f384,f3176]) ).
fof(f1126,plain,
( ! [X0] :
( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
| subclass(singleton_relation,X0) )
| ~ spl0_41
| ~ spl0_134 ),
inference(superposition,[],[f1084,f386]) ).
fof(f3174,plain,
( spl0_320
| ~ spl0_97
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1121,f1083,f731,f3172]) ).
fof(f1121,plain,
( ! [X0,X1] :
( subclass(intersection(singleton_relation,X0),X1)
| member(not_subclass_element(intersection(singleton_relation,X0),X1),element_relation) )
| ~ spl0_97
| ~ spl0_134 ),
inference(resolution,[],[f1084,f732]) ).
fof(f3168,plain,
( spl0_319
| ~ spl0_103
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1120,f1083,f761,f3166]) ).
fof(f1120,plain,
( ! [X0,X1] :
( subclass(intersection(identity_relation,X0),X1)
| member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
| ~ spl0_103
| ~ spl0_134 ),
inference(resolution,[],[f1084,f762]) ).
fof(f3164,plain,
( spl0_318
| ~ spl0_22
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1078,f1020,f295,f3162]) ).
fof(f3162,plain,
( spl0_318
<=> ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f1078,plain,
( ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X1,X0)) )
| ~ spl0_22
| ~ spl0_132 ),
inference(resolution,[],[f1021,f296]) ).
fof(f3155,plain,
( spl0_317
| ~ spl0_22
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1075,f1016,f295,f3153]) ).
fof(f3153,plain,
( spl0_317
<=> ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f1075,plain,
( ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X0,X1)) )
| ~ spl0_22
| ~ spl0_131 ),
inference(resolution,[],[f1017,f296]) ).
fof(f3151,plain,
( spl0_316
| ~ spl0_20
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1066,f1012,f287,f3149]) ).
fof(f1066,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| subclass(X0,X2)
| ~ member(not_subclass_element(X0,X2),X1) )
| ~ spl0_20
| ~ spl0_130 ),
inference(resolution,[],[f1013,f288]) ).
fof(f3147,plain,
( spl0_315
| ~ spl0_31
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f976,f919,f335,f3145]) ).
fof(f3145,plain,
( spl0_315
<=> ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| null_class = X0
| member(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f976,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| null_class = X0
| member(regular(X0),X1) )
| ~ spl0_31
| ~ spl0_116 ),
inference(resolution,[],[f920,f336]) ).
fof(f3143,plain,
( spl0_314
| ~ spl0_32
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f975,f919,f339,f3141]) ).
fof(f3141,plain,
( spl0_314
<=> ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| null_class = X0
| member(regular(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f975,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| null_class = X0
| member(regular(X0),X2) )
| ~ spl0_32
| ~ spl0_116 ),
inference(resolution,[],[f920,f340]) ).
fof(f3139,plain,
( spl0_313
| ~ spl0_28
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f877,f823,f323,f3137]) ).
fof(f877,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
| subclass(X0,cross_product(universal_class,universal_class)) )
| ~ spl0_28
| ~ spl0_111 ),
inference(resolution,[],[f824,f324]) ).
fof(f3120,plain,
( spl0_312
| ~ spl0_235
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3051,f2923,f2310,f3118]) ).
fof(f2923,plain,
( spl0_299
<=> ! [X0] :
( null_class = intersection(X0,identity_relation)
| member(regular(intersection(X0,identity_relation)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f3051,plain,
( ! [X0] :
( member(regular(intersection(X0,singleton_relation)),subset_relation)
| null_class = intersection(X0,singleton_relation) )
| ~ spl0_235
| ~ spl0_299 ),
inference(forward_demodulation,[],[f2926,f2312]) ).
fof(f2926,plain,
( ! [X0] :
( null_class = intersection(X0,singleton_relation)
| member(regular(intersection(X0,identity_relation)),subset_relation) )
| ~ spl0_235
| ~ spl0_299 ),
inference(forward_demodulation,[],[f2924,f2312]) ).
fof(f2924,plain,
( ! [X0] :
( null_class = intersection(X0,identity_relation)
| member(regular(intersection(X0,identity_relation)),subset_relation) )
| ~ spl0_299 ),
inference(avatar_component_clause,[],[f2923]) ).
fof(f3108,plain,
( ~ spl0_311
| ~ spl0_4
| ~ spl0_9
| ~ spl0_262
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f2586,f2499,f2452,f240,f219,f3105]) ).
fof(f3105,plain,
( spl0_311
<=> subclass(universal_class,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f2586,plain,
( ~ subclass(universal_class,null_class)
| ~ spl0_4
| ~ spl0_9
| ~ spl0_262
| ~ spl0_268 ),
inference(forward_demodulation,[],[f2565,f2484]) ).
fof(f2565,plain,
( ~ subclass(universal_class,complement(universal_class))
| ~ spl0_9
| ~ spl0_268 ),
inference(resolution,[],[f2500,f241]) ).
fof(f3094,plain,
( spl0_310
| ~ spl0_235
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f2938,f2935,f2310,f3092]) ).
fof(f2935,plain,
( spl0_301
<=> ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f2938,plain,
( ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),subset_relation) )
| ~ spl0_235
| ~ spl0_301 ),
inference(forward_demodulation,[],[f2936,f2312]) ).
fof(f2936,plain,
( ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),subset_relation) )
| ~ spl0_301 ),
inference(avatar_component_clause,[],[f2935]) ).
fof(f3073,plain,
( spl0_309
| ~ spl0_235
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f3057,f2851,f2310,f3070]) ).
fof(f2851,plain,
( spl0_296
<=> member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f3057,plain,
( member(regular(singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_235
| ~ spl0_296 ),
inference(forward_demodulation,[],[f2853,f2312]) ).
fof(f2853,plain,
( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_296 ),
inference(avatar_component_clause,[],[f2851]) ).
fof(f3068,plain,
( spl0_308
| ~ spl0_235
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f3052,f2830,f2310,f3065]) ).
fof(f2830,plain,
( spl0_295
<=> member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f3052,plain,
( member(regular(singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
| ~ spl0_235
| ~ spl0_295 ),
inference(forward_demodulation,[],[f2832,f2312]) ).
fof(f2832,plain,
( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
| ~ spl0_295 ),
inference(avatar_component_clause,[],[f2830]) ).
fof(f3063,plain,
( ~ spl0_307
| ~ spl0_111
| spl0_298 ),
inference(avatar_split_clause,[],[f2919,f2915,f823,f3060]) ).
fof(f3060,plain,
( spl0_307
<=> member(singleton_relation,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f2915,plain,
( spl0_298
<=> member(singleton_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f2919,plain,
( ~ member(singleton_relation,subset_relation)
| ~ spl0_111
| spl0_298 ),
inference(resolution,[],[f2917,f824]) ).
fof(f2917,plain,
( ~ member(singleton_relation,cross_product(universal_class,universal_class))
| spl0_298 ),
inference(avatar_component_clause,[],[f2915]) ).
fof(f3055,plain,
( spl0_231
| ~ spl0_233
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2864,f2310,f2300,f2282]) ).
fof(f2864,plain,
( null_class = singleton_relation
| ~ spl0_233
| ~ spl0_235 ),
inference(forward_demodulation,[],[f2302,f2312]) ).
fof(f2302,plain,
( null_class = identity_relation
| ~ spl0_233 ),
inference(avatar_component_clause,[],[f2300]) ).
fof(f3044,plain,
( spl0_306
| ~ spl0_231
| ~ spl0_235
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f2928,f2923,f2310,f2282,f3042]) ).
fof(f3042,plain,
( spl0_306
<=> ! [X0] :
( member(regular(intersection(X0,singleton_relation)),subset_relation)
| singleton_relation = intersection(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f2928,plain,
( ! [X0] :
( member(regular(intersection(X0,singleton_relation)),subset_relation)
| singleton_relation = intersection(X0,singleton_relation) )
| ~ spl0_231
| ~ spl0_235
| ~ spl0_299 ),
inference(forward_demodulation,[],[f2927,f2312]) ).
fof(f2927,plain,
( ! [X0] :
( singleton_relation = intersection(X0,singleton_relation)
| member(regular(intersection(X0,identity_relation)),subset_relation) )
| ~ spl0_231
| ~ spl0_235
| ~ spl0_299 ),
inference(forward_demodulation,[],[f2926,f2284]) ).
fof(f2284,plain,
( null_class = singleton_relation
| ~ spl0_231 ),
inference(avatar_component_clause,[],[f2282]) ).
fof(f2955,plain,
( spl0_305
| ~ spl0_9
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1733,f1711,f240,f2953]) ).
fof(f2953,plain,
( spl0_305
<=> ! [X0,X1] :
( member(regular(cross_product(X0,X1)),universal_class)
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f1733,plain,
( ! [X0,X1] :
( member(regular(cross_product(X0,X1)),universal_class)
| cross_product(X0,X1) = null_class )
| ~ spl0_9
| ~ spl0_198 ),
inference(superposition,[],[f241,f1712]) ).
fof(f2951,plain,
( spl0_304
| ~ spl0_68
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1409,f1369,f560,f2949]) ).
fof(f2949,plain,
( spl0_304
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(X0,X1))
| ~ member(X2,universal_class)
| member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f1409,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(X0,X1))
| ~ member(X2,universal_class)
| member(X2,X0) )
| ~ spl0_68
| ~ spl0_165 ),
inference(resolution,[],[f1370,f561]) ).
fof(f2947,plain,
( ~ spl0_303
| ~ spl0_3
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f2920,f2503,f214,f2944]) ).
fof(f2944,plain,
( spl0_303
<=> inductive(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f214,plain,
( spl0_3
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f2920,plain,
( ~ inductive(choice)
| ~ spl0_3
| ~ spl0_269 ),
inference(resolution,[],[f2504,f216]) ).
fof(f216,plain,
( function(choice)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f2942,plain,
( spl0_302
| ~ spl0_97
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1070,f1012,f731,f2940]) ).
fof(f1070,plain,
( ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),element_relation) )
| ~ spl0_97
| ~ spl0_130 ),
inference(resolution,[],[f1013,f732]) ).
fof(f2937,plain,
( spl0_301
| ~ spl0_103
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1069,f1012,f761,f2935]) ).
fof(f1069,plain,
( ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),subset_relation) )
| ~ spl0_103
| ~ spl0_130 ),
inference(resolution,[],[f1013,f762]) ).
fof(f2932,plain,
( spl0_300
| ~ spl0_97
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1052,f1008,f731,f2930]) ).
fof(f1052,plain,
( ! [X0] :
( null_class = intersection(X0,singleton_relation)
| member(regular(intersection(X0,singleton_relation)),element_relation) )
| ~ spl0_97
| ~ spl0_129 ),
inference(resolution,[],[f1009,f732]) ).
fof(f2925,plain,
( spl0_299
| ~ spl0_103
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1051,f1008,f761,f2923]) ).
fof(f1051,plain,
( ! [X0] :
( null_class = intersection(X0,identity_relation)
| member(regular(intersection(X0,identity_relation)),subset_relation) )
| ~ spl0_103
| ~ spl0_129 ),
inference(resolution,[],[f1009,f762]) ).
fof(f2918,plain,
( ~ spl0_298
| ~ spl0_235
| spl0_257 ),
inference(avatar_split_clause,[],[f2911,f2423,f2310,f2915]) ).
fof(f2423,plain,
( spl0_257
<=> member(identity_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f2911,plain,
( ~ member(singleton_relation,cross_product(universal_class,universal_class))
| ~ spl0_235
| spl0_257 ),
inference(forward_demodulation,[],[f2424,f2312]) ).
fof(f2424,plain,
( ~ member(identity_relation,cross_product(universal_class,universal_class))
| spl0_257 ),
inference(avatar_component_clause,[],[f2423]) ).
fof(f2907,plain,
( spl0_297
| ~ spl0_38
| ~ spl0_235
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f2892,f2423,f2310,f372,f2905]) ).
fof(f2905,plain,
( spl0_297
<=> ! [X0] :
( member(singleton_relation,X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f2892,plain,
( ! [X0] :
( member(singleton_relation,X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) )
| ~ spl0_38
| ~ spl0_235
| ~ spl0_257 ),
inference(forward_demodulation,[],[f2886,f2312]) ).
fof(f2886,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(identity_relation,X0) )
| ~ spl0_38
| ~ spl0_257 ),
inference(resolution,[],[f2425,f373]) ).
fof(f2425,plain,
( member(identity_relation,cross_product(universal_class,universal_class))
| ~ spl0_257 ),
inference(avatar_component_clause,[],[f2423]) ).
fof(f2854,plain,
( spl0_233
| spl0_296
| ~ spl0_43
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1042,f1004,f393,f2851,f2300]) ).
fof(f1042,plain,
( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| null_class = identity_relation
| ~ spl0_43
| ~ spl0_128 ),
inference(superposition,[],[f1005,f395]) ).
fof(f2833,plain,
( spl0_231
| spl0_295
| ~ spl0_41
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1041,f1004,f384,f2830,f2282]) ).
fof(f1041,plain,
( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
| null_class = singleton_relation
| ~ spl0_41
| ~ spl0_128 ),
inference(superposition,[],[f1005,f386]) ).
fof(f2828,plain,
( spl0_294
| ~ spl0_97
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1036,f1004,f731,f2826]) ).
fof(f1036,plain,
( ! [X0] :
( null_class = intersection(singleton_relation,X0)
| member(regular(intersection(singleton_relation,X0)),element_relation) )
| ~ spl0_97
| ~ spl0_128 ),
inference(resolution,[],[f1005,f732]) ).
fof(f2824,plain,
( spl0_293
| ~ spl0_103
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1035,f1004,f761,f2822]) ).
fof(f1035,plain,
( ! [X0] :
( null_class = intersection(identity_relation,X0)
| member(regular(intersection(identity_relation,X0)),subset_relation) )
| ~ spl0_103
| ~ spl0_128 ),
inference(resolution,[],[f1005,f762]) ).
fof(f2820,plain,
( spl0_292
| ~ spl0_20
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f977,f919,f287,f2818]) ).
fof(f977,plain,
( ! [X0,X1] :
( ~ subclass(X0,complement(X1))
| null_class = X0
| ~ member(regular(X0),X1) )
| ~ spl0_20
| ~ spl0_116 ),
inference(resolution,[],[f920,f288]) ).
fof(f2816,plain,
( spl0_291
| ~ spl0_38
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f876,f823,f372,f2814]) ).
fof(f876,plain,
( ! [X0,X1] :
( ~ member(X0,subset_relation)
| ~ subclass(cross_product(universal_class,universal_class),X1)
| member(X0,X1) )
| ~ spl0_38
| ~ spl0_111 ),
inference(resolution,[],[f824,f373]) ).
fof(f2812,plain,
( spl0_290
| ~ spl0_38
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f845,f802,f372,f2810]) ).
fof(f2810,plain,
( spl0_290
<=> ! [X2,X0,X1,X3] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(unordered_pair(X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f845,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(unordered_pair(X2,X3),X1) )
| ~ spl0_38
| ~ spl0_106 ),
inference(resolution,[],[f803,f373]) ).
fof(f2749,plain,
( spl0_288
| ~ spl0_289
| ~ spl0_61
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1412,f1369,f524,f2746,f2743]) ).
fof(f2743,plain,
( spl0_288
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(X0,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f2746,plain,
( spl0_289
<=> subclass(domain_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f1412,plain,
( ! [X0] :
( ~ subclass(domain_relation,element_relation)
| ~ member(X0,universal_class)
| member(X0,domain_of(X0)) )
| ~ spl0_61
| ~ spl0_165 ),
inference(resolution,[],[f1370,f525]) ).
fof(f2741,plain,
( spl0_287
| ~ spl0_27
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1308,f1290,f319,f2739]) ).
fof(f1308,plain,
( ! [X0] :
( member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) )
| ~ spl0_27
| ~ spl0_157 ),
inference(duplicate_literal_removal,[],[f1301]) ).
fof(f1301,plain,
( ! [X0] :
( member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0))
| subclass(universal_class,complement(X0)) )
| ~ spl0_27
| ~ spl0_157 ),
inference(resolution,[],[f1291,f320]) ).
fof(f2737,plain,
( spl0_286
| ~ spl0_76
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1125,f1083,f608,f2735]) ).
fof(f1125,plain,
( ! [X0] :
( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
| subclass(subset_relation,X0) )
| ~ spl0_76
| ~ spl0_134 ),
inference(superposition,[],[f1084,f610]) ).
fof(f2733,plain,
( spl0_285
| ~ spl0_97
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f981,f919,f731,f2731]) ).
fof(f981,plain,
( ! [X0] :
( ~ subclass(X0,singleton_relation)
| null_class = X0
| member(regular(X0),element_relation) )
| ~ spl0_97
| ~ spl0_116 ),
inference(resolution,[],[f920,f732]) ).
fof(f2729,plain,
( spl0_284
| ~ spl0_4
| ~ spl0_262
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2488,f2456,f2452,f219,f2727]) ).
fof(f2456,plain,
( spl0_263
<=> ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f2488,plain,
( ! [X0] : subclass(null_class,X0)
| ~ spl0_4
| ~ spl0_262
| ~ spl0_263 ),
inference(forward_demodulation,[],[f2486,f2484]) ).
fof(f2486,plain,
( ! [X0] : subclass(complement(universal_class),X0)
| ~ spl0_4
| ~ spl0_263 ),
inference(resolution,[],[f2457,f220]) ).
fof(f2457,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1) )
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f2456]) ).
fof(f2725,plain,
( spl0_283
| ~ spl0_103
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f980,f919,f761,f2723]) ).
fof(f980,plain,
( ! [X0] :
( ~ subclass(X0,identity_relation)
| null_class = X0
| member(regular(X0),subset_relation) )
| ~ spl0_103
| ~ spl0_116 ),
inference(resolution,[],[f920,f762]) ).
fof(f2713,plain,
( spl0_281
| ~ spl0_274
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f2712,f2698,f2535,f2704]) ).
fof(f2704,plain,
( spl0_281
<=> member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f2712,plain,
( member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl0_274
| ~ spl0_280 ),
inference(forward_demodulation,[],[f2700,f2537]) ).
fof(f2537,plain,
( null_class = subset_relation
| ~ spl0_274 ),
inference(avatar_component_clause,[],[f2535]) ).
fof(f2711,plain,
( spl0_282
| spl0_280
| ~ spl0_34
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f861,f815,f347,f2698,f2709]) ).
fof(f2709,plain,
( spl0_282
<=> ! [X0] : ~ inductive(flip(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f347,plain,
( spl0_34
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f861,plain,
( ! [X0] :
( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ inductive(flip(X0)) )
| ~ spl0_34
| ~ spl0_109 ),
inference(resolution,[],[f816,f348]) ).
fof(f348,plain,
( ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f2707,plain,
( ~ spl0_281
| ~ spl0_274
| spl0_280 ),
inference(avatar_split_clause,[],[f2702,f2698,f2535,f2704]) ).
fof(f2702,plain,
( ~ member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl0_274
| spl0_280 ),
inference(forward_demodulation,[],[f2699,f2537]) ).
fof(f2699,plain,
( ~ member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
| spl0_280 ),
inference(avatar_component_clause,[],[f2698]) ).
fof(f2701,plain,
( spl0_279
| spl0_280
| ~ spl0_33
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f860,f815,f343,f2698,f2695]) ).
fof(f2695,plain,
( spl0_279
<=> ! [X0] : ~ inductive(rotate(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f343,plain,
( spl0_33
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f860,plain,
( ! [X0] :
( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ inductive(rotate(X0)) )
| ~ spl0_33
| ~ spl0_109 ),
inference(resolution,[],[f816,f344]) ).
fof(f344,plain,
( ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f2691,plain,
( spl0_278
| ~ spl0_31
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f849,f802,f335,f2689]) ).
fof(f2689,plain,
( spl0_278
<=> ! [X2,X0,X1,X3] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f849,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X0) )
| ~ spl0_31
| ~ spl0_106 ),
inference(resolution,[],[f803,f336]) ).
fof(f2687,plain,
( spl0_277
| ~ spl0_32
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f848,f802,f339,f2685]) ).
fof(f2685,plain,
( spl0_277
<=> ! [X2,X0,X1,X3] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f848,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X1) )
| ~ spl0_32
| ~ spl0_106 ),
inference(resolution,[],[f803,f340]) ).
fof(f2560,plain,
( spl0_276
| ~ spl0_4
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1250,f1243,f219,f2558]) ).
fof(f1250,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,universal_class) )
| ~ spl0_4
| ~ spl0_151 ),
inference(resolution,[],[f1244,f220]) ).
fof(f2542,plain,
( spl0_274
| spl0_275
| ~ spl0_76
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1040,f1004,f608,f2539,f2535]) ).
fof(f1040,plain,
( member(regular(subset_relation),cross_product(universal_class,universal_class))
| null_class = subset_relation
| ~ spl0_76
| ~ spl0_128 ),
inference(superposition,[],[f1005,f610]) ).
fof(f2531,plain,
( spl0_273
| ~ spl0_20
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f992,f955,f287,f2529]) ).
fof(f992,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| ~ member(X0,compose(element_relation,complement(identity_relation))) )
| ~ spl0_20
| ~ spl0_124 ),
inference(resolution,[],[f956,f288]) ).
fof(f2527,plain,
( ~ spl0_272
| spl0_271
| ~ spl0_25
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f870,f815,f308,f2518,f2524]) ).
fof(f2524,plain,
( spl0_272
<=> inductive(application_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f2518,plain,
( spl0_271
<=> member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f308,plain,
( spl0_25
<=> subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f870,plain,
( member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ inductive(application_function)
| ~ spl0_25
| ~ spl0_109 ),
inference(resolution,[],[f816,f310]) ).
fof(f310,plain,
( subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f2521,plain,
( ~ spl0_270
| spl0_271
| ~ spl0_24
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f868,f815,f303,f2518,f2514]) ).
fof(f2514,plain,
( spl0_270
<=> inductive(composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f868,plain,
( member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ inductive(composition_function)
| ~ spl0_24
| ~ spl0_109 ),
inference(resolution,[],[f816,f305]) ).
fof(f305,plain,
( subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f2505,plain,
( spl0_269
| spl0_182
| ~ spl0_22
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f856,f815,f295,f1538,f2503]) ).
fof(f856,plain,
( ! [X0] :
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(X0)
| ~ function(X0) )
| ~ spl0_22
| ~ spl0_109 ),
inference(resolution,[],[f816,f296]) ).
fof(f2501,plain,
( spl0_268
| ~ spl0_20
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f850,f802,f287,f2499]) ).
fof(f850,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(unordered_pair(X1,X2),X0) )
| ~ spl0_20
| ~ spl0_106 ),
inference(resolution,[],[f803,f288]) ).
fof(f2497,plain,
( ~ spl0_267
| ~ spl0_111
| spl0_230 ),
inference(avatar_split_clause,[],[f2280,f2276,f823,f2494]) ).
fof(f2494,plain,
( spl0_267
<=> member(omega,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f2276,plain,
( spl0_230
<=> member(omega,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f2280,plain,
( ~ member(omega,subset_relation)
| ~ spl0_111
| spl0_230 ),
inference(resolution,[],[f2277,f824]) ).
fof(f2277,plain,
( ~ member(omega,cross_product(universal_class,universal_class))
| spl0_230 ),
inference(avatar_component_clause,[],[f2276]) ).
fof(f2492,plain,
( spl0_266
| ~ spl0_72
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f833,f802,f584,f2490]) ).
fof(f2490,plain,
( spl0_266
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,compose_class(X0))
| compose(X0,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f833,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,compose_class(X0))
| compose(X0,X1) = X2 )
| ~ spl0_72
| ~ spl0_106 ),
inference(resolution,[],[f803,f585]) ).
fof(f2481,plain,
( spl0_265
| ~ spl0_38
| ~ spl0_182 ),
inference(avatar_split_clause,[],[f2429,f1538,f372,f2479]) ).
fof(f2429,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(null_class,X0) )
| ~ spl0_38
| ~ spl0_182 ),
inference(resolution,[],[f1539,f373]) ).
fof(f1539,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f1538]) ).
fof(f2469,plain,
( spl0_264
| ~ spl0_43
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2251,f2227,f393,f2466]) ).
fof(f2251,plain,
( subclass(identity_relation,subset_relation)
| ~ spl0_43
| ~ spl0_224 ),
inference(superposition,[],[f2228,f395]) ).
fof(f2458,plain,
( spl0_263
| ~ spl0_115
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1071,f1012,f915,f2456]) ).
fof(f1071,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1) )
| ~ spl0_115
| ~ spl0_130 ),
inference(duplicate_literal_removal,[],[f1060]) ).
fof(f1060,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1)
| subclass(complement(X0),X1) )
| ~ spl0_115
| ~ spl0_130 ),
inference(resolution,[],[f1013,f916]) ).
fof(f2454,plain,
( spl0_262
| ~ spl0_112
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f982,f919,f884,f2452]) ).
fof(f982,plain,
( ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class )
| ~ spl0_112
| ~ spl0_116 ),
inference(duplicate_literal_removal,[],[f971]) ).
fof(f971,plain,
( ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class
| complement(X0) = null_class )
| ~ spl0_112
| ~ spl0_116 ),
inference(resolution,[],[f920,f885]) ).
fof(f2450,plain,
( spl0_261
| ~ spl0_21
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f911,f892,f291,f2448]) ).
fof(f2448,plain,
( spl0_261
<=> ! [X0,X1] :
( function(compose(X0,X1))
| ~ single_valued_class(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f291,plain,
( spl0_21
<=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f911,plain,
( ! [X0,X1] :
( function(compose(X0,X1))
| ~ single_valued_class(compose(X0,X1)) )
| ~ spl0_21
| ~ spl0_114 ),
inference(resolution,[],[f893,f292]) ).
fof(f292,plain,
( ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class))
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f2446,plain,
( ~ spl0_259
| spl0_260
| ~ spl0_6
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f906,f892,f228,f2443,f2439]) ).
fof(f2439,plain,
( spl0_259
<=> single_valued_class(cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f2443,plain,
( spl0_260
<=> function(cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f906,plain,
( function(cross_product(universal_class,universal_class))
| ~ single_valued_class(cross_product(universal_class,universal_class))
| ~ spl0_6
| ~ spl0_114 ),
inference(resolution,[],[f893,f229]) ).
fof(f2435,plain,
( ~ spl0_258
| ~ spl0_111
| spl0_257 ),
inference(avatar_split_clause,[],[f2430,f2423,f823,f2432]) ).
fof(f2432,plain,
( spl0_258
<=> member(identity_relation,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f2430,plain,
( ~ member(identity_relation,subset_relation)
| ~ spl0_111
| spl0_257 ),
inference(resolution,[],[f2424,f824]) ).
fof(f2426,plain,
( spl0_257
| ~ spl0_182
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2421,f2300,f1538,f2423]) ).
fof(f2421,plain,
( member(identity_relation,cross_product(universal_class,universal_class))
| ~ spl0_182
| ~ spl0_233 ),
inference(forward_demodulation,[],[f1539,f2302]) ).
fof(f2416,plain,
( spl0_256
| spl0_182
| ~ spl0_18
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f867,f815,f279,f1538,f2414]) ).
fof(f2414,plain,
( spl0_256
<=> ! [X0] : ~ inductive(compose_class(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f279,plain,
( spl0_18
<=> ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f867,plain,
( ! [X0] :
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(compose_class(X0)) )
| ~ spl0_18
| ~ spl0_109 ),
inference(resolution,[],[f816,f280]) ).
fof(f280,plain,
( ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class))
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f2412,plain,
( spl0_254
| ~ spl0_255
| ~ spl0_97
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f853,f802,f731,f2409,f2406]) ).
fof(f2406,plain,
( spl0_254
<=> ! [X0,X1] : member(unordered_pair(X0,X1),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f2409,plain,
( spl0_255
<=> subclass(universal_class,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f853,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,singleton_relation)
| member(unordered_pair(X0,X1),element_relation) )
| ~ spl0_97
| ~ spl0_106 ),
inference(resolution,[],[f803,f732]) ).
fof(f2404,plain,
( spl0_252
| ~ spl0_253
| ~ spl0_103
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f852,f802,f761,f2401,f2398]) ).
fof(f2398,plain,
( spl0_252
<=> ! [X0,X1] : member(unordered_pair(X0,X1),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f2401,plain,
( spl0_253
<=> subclass(universal_class,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f852,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,identity_relation)
| member(unordered_pair(X0,X1),subset_relation) )
| ~ spl0_103
| ~ spl0_106 ),
inference(resolution,[],[f803,f762]) ).
fof(f2396,plain,
( spl0_251
| ~ spl0_41
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2250,f2227,f384,f2393]) ).
fof(f2250,plain,
( subclass(singleton_relation,element_relation)
| ~ spl0_41
| ~ spl0_224 ),
inference(superposition,[],[f2228,f386]) ).
fof(f2391,plain,
( spl0_249
| ~ spl0_250
| ~ spl0_87
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f837,f802,f673,f2388,f2385]) ).
fof(f2385,plain,
( spl0_249
<=> ! [X2,X0,X1] : compose(X0,X1) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f2388,plain,
( spl0_250
<=> subclass(universal_class,composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f837,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,composition_function)
| compose(X0,X1) = X2 )
| ~ spl0_87
| ~ spl0_106 ),
inference(resolution,[],[f803,f674]) ).
fof(f2383,plain,
( spl0_248
| ~ spl0_67
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f827,f802,f556,f2381]) ).
fof(f2381,plain,
( spl0_248
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f827,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X1) )
| ~ spl0_67
| ~ spl0_106 ),
inference(resolution,[],[f803,f557]) ).
fof(f2379,plain,
( spl0_247
| ~ spl0_68
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f826,f802,f560,f2377]) ).
fof(f2377,plain,
( spl0_247
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f826,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X0) )
| ~ spl0_68
| ~ spl0_106 ),
inference(resolution,[],[f803,f561]) ).
fof(f2374,plain,
( spl0_245
| ~ spl0_246
| ~ spl0_40
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f782,f389,f380,f2371,f2368]) ).
fof(f2368,plain,
( spl0_245
<=> ! [X0] :
( member(null_class,X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f2371,plain,
( spl0_246
<=> inductive(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f389,plain,
( spl0_42
<=> ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f782,plain,
( ! [X0] :
( ~ inductive(null_class)
| member(null_class,X0)
| null_class = X0 )
| ~ spl0_40
| ~ spl0_42 ),
inference(superposition,[],[f390,f381]) ).
fof(f390,plain,
( ! [X0,X1] :
( ~ inductive(intersection(X0,X1))
| member(null_class,X0) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f2366,plain,
( spl0_244
| ~ spl0_27
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f774,f761,f319,f2364]) ).
fof(f774,plain,
( ! [X0] :
( member(not_subclass_element(identity_relation,X0),subset_relation)
| subclass(identity_relation,X0) )
| ~ spl0_27
| ~ spl0_103 ),
inference(resolution,[],[f762,f320]) ).
fof(f2362,plain,
( spl0_243
| ~ spl0_27
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f770,f731,f319,f2360]) ).
fof(f770,plain,
( ! [X0] :
( member(not_subclass_element(singleton_relation,X0),element_relation)
| subclass(singleton_relation,X0) )
| ~ spl0_27
| ~ spl0_97 ),
inference(resolution,[],[f732,f320]) ).
fof(f2358,plain,
( spl0_242
| ~ spl0_37
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f537,f511,f359,f2356]) ).
fof(f2356,plain,
( spl0_242
<=> ! [X0] :
( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
| ~ one_to_one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f511,plain,
( spl0_59
<=> ! [X0] :
( single_valued_class(X0)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f537,plain,
( ! [X0] :
( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
| ~ one_to_one(X0) )
| ~ spl0_37
| ~ spl0_59 ),
inference(resolution,[],[f512,f360]) ).
fof(f512,plain,
( ! [X0] :
( ~ function(X0)
| single_valued_class(X0) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f511]) ).
fof(f2354,plain,
( ~ spl0_241
| spl0_182
| ~ spl0_14
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f869,f815,f262,f1538,f2351]) ).
fof(f2351,plain,
( spl0_241
<=> inductive(domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f869,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(domain_relation)
| ~ spl0_14
| ~ spl0_109 ),
inference(resolution,[],[f816,f264]) ).
fof(f2349,plain,
( ~ spl0_240
| spl0_182
| ~ spl0_11
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f862,f815,f249,f1538,f2346]) ).
fof(f2346,plain,
( spl0_240
<=> inductive(successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f249,plain,
( spl0_11
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f862,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(successor_relation)
| ~ spl0_11
| ~ spl0_109 ),
inference(resolution,[],[f816,f251]) ).
fof(f251,plain,
( subclass(successor_relation,cross_product(universal_class,universal_class))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f2344,plain,
( spl0_238
| ~ spl0_239
| ~ spl0_86
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f836,f802,f669,f2341,f2338]) ).
fof(f2338,plain,
( spl0_238
<=> ! [X0,X1] : member(X0,domain_of(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f2341,plain,
( spl0_239
<=> subclass(universal_class,application_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f836,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,application_function)
| member(X0,domain_of(X1)) )
| ~ spl0_86
| ~ spl0_106 ),
inference(resolution,[],[f803,f670]) ).
fof(f2336,plain,
( spl0_236
| ~ spl0_237
| ~ spl0_64
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f834,f802,f539,f2333,f2330]) ).
fof(f2330,plain,
( spl0_236
<=> ! [X0,X1] : domain_of(X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f2333,plain,
( spl0_237
<=> subclass(universal_class,domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f834,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,domain_relation)
| domain_of(X0) = X1 )
| ~ spl0_64
| ~ spl0_106 ),
inference(resolution,[],[f803,f540]) ).
fof(f2313,plain,
( spl0_235
| ~ spl0_231
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2308,f2300,f2282,f2310]) ).
fof(f2308,plain,
( identity_relation = singleton_relation
| ~ spl0_231
| ~ spl0_233 ),
inference(forward_demodulation,[],[f2302,f2284]) ).
fof(f2307,plain,
( spl0_233
| spl0_234
| ~ spl0_23
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f777,f761,f299,f2304,f2300]) ).
fof(f777,plain,
( member(regular(identity_relation),subset_relation)
| null_class = identity_relation
| ~ spl0_23
| ~ spl0_103 ),
inference(resolution,[],[f762,f300]) ).
fof(f2289,plain,
( spl0_231
| spl0_232
| ~ spl0_23
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f773,f731,f299,f2286,f2282]) ).
fof(f773,plain,
( member(regular(singleton_relation),element_relation)
| null_class = singleton_relation
| ~ spl0_23
| ~ spl0_97 ),
inference(resolution,[],[f732,f300]) ).
fof(f2279,plain,
( ~ spl0_229
| spl0_230
| ~ spl0_22
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f766,f439,f295,f2276,f2272]) ).
fof(f2272,plain,
( spl0_229
<=> function(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f439,plain,
( spl0_47
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(omega,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f766,plain,
( member(omega,cross_product(universal_class,universal_class))
| ~ function(universal_class)
| ~ spl0_22
| ~ spl0_47 ),
inference(resolution,[],[f440,f296]) ).
fof(f440,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(omega,X0) )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f2267,plain,
( spl0_228
| ~ spl0_38
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f2171,f636,f372,f2265]) ).
fof(f2171,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(null_class,X0) )
| ~ spl0_38
| ~ spl0_80 ),
inference(resolution,[],[f637,f373]) ).
fof(f637,plain,
( member(null_class,universal_class)
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f636]) ).
fof(f2263,plain,
( spl0_227
| ~ spl0_18
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f912,f892,f279,f2261]) ).
fof(f2261,plain,
( spl0_227
<=> ! [X0] :
( function(compose_class(X0))
| ~ single_valued_class(compose_class(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f912,plain,
( ! [X0] :
( function(compose_class(X0))
| ~ single_valued_class(compose_class(X0)) )
| ~ spl0_18
| ~ spl0_114 ),
inference(resolution,[],[f893,f280]) ).
fof(f2259,plain,
( spl0_225
| ~ spl0_226
| ~ spl0_61
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f829,f802,f524,f2256,f2253]) ).
fof(f2253,plain,
( spl0_225
<=> ! [X0,X1] : member(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f2256,plain,
( spl0_226
<=> subclass(universal_class,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f829,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,element_relation)
| member(X0,X1) )
| ~ spl0_61
| ~ spl0_106 ),
inference(resolution,[],[f803,f525]) ).
fof(f2229,plain,
( spl0_224
| ~ spl0_28
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1146,f1087,f323,f2227]) ).
fof(f1146,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X1)
| ~ spl0_28
| ~ spl0_135 ),
inference(duplicate_literal_removal,[],[f1129]) ).
fof(f1129,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) )
| ~ spl0_28
| ~ spl0_135 ),
inference(resolution,[],[f1088,f324]) ).
fof(f2225,plain,
( spl0_223
| ~ spl0_28
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1128,f1083,f323,f2223]) ).
fof(f1128,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X0)
| ~ spl0_28
| ~ spl0_134 ),
inference(duplicate_literal_removal,[],[f1111]) ).
fof(f1111,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) )
| ~ spl0_28
| ~ spl0_134 ),
inference(resolution,[],[f1084,f324]) ).
fof(f2141,plain,
( ~ spl0_2
| ~ spl0_222 ),
inference(avatar_contradiction_clause,[],[f2140]) ).
fof(f2140,plain,
( $false
| ~ spl0_2
| ~ spl0_222 ),
inference(resolution,[],[f2138,f211]) ).
fof(f211,plain,
( inductive(omega)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f2138,plain,
( ! [X0] : ~ inductive(X0)
| ~ spl0_222 ),
inference(avatar_component_clause,[],[f2137]) ).
fof(f2137,plain,
( spl0_222
<=> ! [X0] : ~ inductive(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f2139,plain,
( spl0_222
| spl0_80
| ~ spl0_4
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f854,f815,f219,f636,f2137]) ).
fof(f854,plain,
( ! [X0] :
( member(null_class,universal_class)
| ~ inductive(X0) )
| ~ spl0_4
| ~ spl0_109 ),
inference(resolution,[],[f816,f220]) ).
fof(f2126,plain,
( spl0_221
| ~ spl0_90
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f706,f702,f686,f2124]) ).
fof(f706,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) )
| ~ spl0_90
| ~ spl0_93 ),
inference(resolution,[],[f703,f687]) ).
fof(f2122,plain,
( spl0_220
| ~ spl0_50
| ~ spl0_90
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f755,f750,f686,f452,f2120]) ).
fof(f2120,plain,
( spl0_220
<=> ! [X2,X4,X0,X3,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class)))))))),universal_class),X0),universal_class)))))))
| ~ homomorphism(X0,X1,X2)
| ~ operation(X4)
| ~ compatible(X3,X1,X4)
| homomorphism(X3,X1,X4)
| ~ operation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f755,plain,
( ! [X2,X3,X0,X1,X4] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class)))))))),universal_class),X0),universal_class)))))))
| ~ homomorphism(X0,X1,X2)
| ~ operation(X4)
| ~ compatible(X3,X1,X4)
| homomorphism(X3,X1,X4)
| ~ operation(X1) )
| ~ spl0_50
| ~ spl0_90
| ~ spl0_101 ),
inference(forward_demodulation,[],[f753,f453]) ).
fof(f753,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ homomorphism(X0,X1,X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
| ~ operation(X4)
| ~ compatible(X3,X1,X4)
| homomorphism(X3,X1,X4)
| ~ operation(X1) )
| ~ spl0_90
| ~ spl0_101 ),
inference(resolution,[],[f751,f687]) ).
fof(f2112,plain,
( spl0_219
| ~ spl0_70
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f754,f750,f568,f2110]) ).
fof(f754,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ homomorphism(X0,X1,X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
| null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) )
| ~ spl0_70
| ~ spl0_101 ),
inference(resolution,[],[f751,f569]) ).
fof(f2099,plain,
( spl0_218
| ~ spl0_84
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f709,f702,f654,f2097]) ).
fof(f709,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_84
| ~ spl0_93 ),
inference(resolution,[],[f703,f655]) ).
fof(f2095,plain,
( spl0_217
| ~ spl0_79
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f659,f654,f628,f2093]) ).
fof(f2093,plain,
( spl0_217
<=> ! [X0,X1] :
( ~ member(cross_product(X0,X1),universal_class)
| cross_product(X0,X1) = null_class
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f659,plain,
( ! [X0,X1] :
( ~ member(cross_product(X0,X1),universal_class)
| cross_product(X0,X1) = null_class
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))))) )
| ~ spl0_79
| ~ spl0_84 ),
inference(resolution,[],[f655,f629]) ).
fof(f2082,plain,
( spl0_216
| ~ spl0_27
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f707,f702,f319,f2080]) ).
fof(f707,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) )
| ~ spl0_27
| ~ spl0_93 ),
inference(resolution,[],[f703,f320]) ).
fof(f2069,plain,
( spl0_215
| ~ spl0_23
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f710,f702,f299,f2067]) ).
fof(f710,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
| null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_23
| ~ spl0_93 ),
inference(resolution,[],[f703,f300]) ).
fof(f2058,plain,
( ~ spl0_214
| spl0_192
| ~ spl0_12
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f775,f761,f254,f1613,f2055]) ).
fof(f2055,plain,
( spl0_214
<=> inductive(identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f775,plain,
( member(null_class,subset_relation)
| ~ inductive(identity_relation)
| ~ spl0_12
| ~ spl0_103 ),
inference(resolution,[],[f762,f255]) ).
fof(f2053,plain,
( spl0_213
| ~ spl0_77
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f748,f745,f613,f2051]) ).
fof(f748,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(X1))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class) )
| ~ spl0_77
| ~ spl0_100 ),
inference(resolution,[],[f746,f614]) ).
fof(f2000,plain,
( spl0_212
| ~ spl0_77
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f743,f739,f613,f1998]) ).
fof(f743,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_77
| ~ spl0_99 ),
inference(resolution,[],[f740,f614]) ).
fof(f1996,plain,
( spl0_211
| ~ spl0_77
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f742,f735,f613,f1994]) ).
fof(f742,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_77
| ~ spl0_98 ),
inference(resolution,[],[f736,f614]) ).
fof(f1947,plain,
( spl0_210
| ~ spl0_77
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f631,f628,f613,f1945]) ).
fof(f1945,plain,
( spl0_210
<=> ! [X0,X3,X2,X1] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
| ~ member(X1,X2)
| ~ member(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f631,plain,
( ! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
| ~ member(X1,X2)
| ~ member(X0,X3) )
| ~ spl0_77
| ~ spl0_79 ),
inference(resolution,[],[f629,f614]) ).
fof(f1937,plain,
( spl0_209
| ~ spl0_40
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f715,f702,f380,f1935]) ).
fof(f715,plain,
( ! [X2,X0,X1] :
( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
| ~ spl0_40
| ~ spl0_93 ),
inference(superposition,[],[f703,f381]) ).
fof(f1925,plain,
( spl0_208
| ~ spl0_70
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f705,f702,f568,f1923]) ).
fof(f705,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class)
| null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_70
| ~ spl0_93 ),
inference(resolution,[],[f703,f569]) ).
fof(f1915,plain,
( spl0_207
| ~ spl0_48
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f658,f654,f444,f1913]) ).
fof(f658,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(X0,X1),universal_class)
| unordered_pair(X0,X1) = null_class
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
| ~ spl0_48
| ~ spl0_84 ),
inference(resolution,[],[f655,f445]) ).
fof(f1908,plain,
( spl0_206
| ~ spl0_40
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f712,f702,f380,f1906]) ).
fof(f712,plain,
( ! [X2,X0,X1] :
( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_40
| ~ spl0_93 ),
inference(superposition,[],[f703,f381]) ).
fof(f1870,plain,
( spl0_205
| ~ spl0_38
| ~ spl0_92 ),
inference(avatar_split_clause,[],[f700,f696,f372,f1868]) ).
fof(f700,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(composition_function,X2)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2) )
| ~ spl0_38
| ~ spl0_92 ),
inference(resolution,[],[f697,f373]) ).
fof(f1814,plain,
( spl0_204
| ~ spl0_50
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f714,f702,f452,f1812]) ).
fof(f714,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) )
| ~ spl0_50
| ~ spl0_93 ),
inference(superposition,[],[f703,f453]) ).
fof(f1810,plain,
( ~ spl0_203
| ~ spl0_12
| spl0_192 ),
inference(avatar_split_clause,[],[f1707,f1613,f254,f1807]) ).
fof(f1807,plain,
( spl0_203
<=> inductive(subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f1707,plain,
( ~ inductive(subset_relation)
| ~ spl0_12
| spl0_192 ),
inference(resolution,[],[f1615,f255]) ).
fof(f1615,plain,
( ~ member(null_class,subset_relation)
| spl0_192 ),
inference(avatar_component_clause,[],[f1613]) ).
fof(f1805,plain,
( spl0_202
| ~ spl0_50
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f711,f702,f452,f1803]) ).
fof(f711,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
| ~ spl0_50
| ~ spl0_93 ),
inference(superposition,[],[f703,f453]) ).
fof(f1795,plain,
( spl0_201
| ~ spl0_12
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f708,f702,f254,f1793]) ).
fof(f708,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
| ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class))))) )
| ~ spl0_12
| ~ spl0_93 ),
inference(resolution,[],[f703,f255]) ).
fof(f1775,plain,
( spl0_200
| ~ spl0_27
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f634,f628,f319,f1773]) ).
fof(f634,plain,
( ! [X2,X0,X1] :
( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
| subclass(cross_product(X0,X1),X2) )
| ~ spl0_27
| ~ spl0_79 ),
inference(resolution,[],[f629,f320]) ).
fof(f1747,plain,
( spl0_199
| ~ spl0_38
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f689,f686,f372,f1745]) ).
fof(f689,plain,
( ! [X2,X3,X0,X1] :
( ~ operation(X0)
| ~ compatible(X1,X2,X0)
| homomorphism(X1,X2,X0)
| ~ operation(X2)
| ~ subclass(domain_of(X2),X3)
| member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3) )
| ~ spl0_38
| ~ spl0_90 ),
inference(resolution,[],[f687,f373]) ).
fof(f1713,plain,
( spl0_198
| ~ spl0_23
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f633,f628,f299,f1711]) ).
fof(f633,plain,
( ! [X0,X1] :
( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
| cross_product(X0,X1) = null_class )
| ~ spl0_23
| ~ spl0_79 ),
inference(resolution,[],[f629,f300]) ).
fof(f1706,plain,
( spl0_197
| ~ spl0_77
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f721,f718,f613,f1704]) ).
fof(f721,plain,
( ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_77
| ~ spl0_94 ),
inference(resolution,[],[f719,f614]) ).
fof(f1662,plain,
( spl0_196
| ~ spl0_31
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f661,f654,f335,f1660]) ).
fof(f661,plain,
( ! [X0,X1] :
( ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = null_class
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0) )
| ~ spl0_31
| ~ spl0_84 ),
inference(resolution,[],[f655,f336]) ).
fof(f1658,plain,
( spl0_195
| ~ spl0_32
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f660,f654,f339,f1656]) ).
fof(f660,plain,
( ! [X0,X1] :
( ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = null_class
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1) )
| ~ spl0_32
| ~ spl0_84 ),
inference(resolution,[],[f655,f340]) ).
fof(f1641,plain,
( spl0_194
| ~ spl0_20
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f662,f654,f287,f1639]) ).
fof(f662,plain,
( ! [X0] :
( ~ member(complement(X0),universal_class)
| complement(X0) = null_class
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0) )
| ~ spl0_20
| ~ spl0_84 ),
inference(resolution,[],[f655,f288]) ).
fof(f1622,plain,
( spl0_193
| ~ spl0_38
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f657,f654,f372,f1620]) ).
fof(f657,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| null_class = X0
| ~ subclass(X0,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
| ~ spl0_38
| ~ spl0_84 ),
inference(resolution,[],[f655,f373]) ).
fof(f1616,plain,
( ~ spl0_192
| ~ spl0_111
| spl0_182 ),
inference(avatar_split_clause,[],[f1546,f1538,f823,f1613]) ).
fof(f1546,plain,
( ~ member(null_class,subset_relation)
| ~ spl0_111
| spl0_182 ),
inference(resolution,[],[f1540,f824]) ).
fof(f1540,plain,
( ~ member(null_class,cross_product(universal_class,universal_class))
| spl0_182 ),
inference(avatar_component_clause,[],[f1538]) ).
fof(f1611,plain,
( spl0_191
| ~ spl0_39
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f535,f532,f376,f1609]) ).
fof(f535,plain,
( ! [X0] :
( ~ inductive(X0)
| ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
| domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 )
| ~ spl0_39
| ~ spl0_63 ),
inference(resolution,[],[f533,f377]) ).
fof(f1599,plain,
( ~ spl0_188
| ~ spl0_189
| spl0_190
| ~ spl0_73
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f616,f608,f588,f1596,f1592,f1588]) ).
fof(f1588,plain,
( spl0_188
<=> function(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1592,plain,
( spl0_189
<=> member(universal_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1596,plain,
( spl0_190
<=> member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f588,plain,
( spl0_73
<=> ! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f616,plain,
( member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
| ~ member(universal_class,universal_class)
| ~ function(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ spl0_73
| ~ spl0_76 ),
inference(superposition,[],[f589,f610]) ).
fof(f589,plain,
( ! [X0,X8] :
( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class)
| ~ member(X0,universal_class)
| ~ function(X8) )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f1586,plain,
( spl0_187
| ~ spl0_28
| ~ spl0_50
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f582,f568,f452,f323,f1584]) ).
fof(f582,plain,
( ! [X0,X1] :
( null_class = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
| ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
| subclass(X0,domain_of(X1)) )
| ~ spl0_28
| ~ spl0_50
| ~ spl0_70 ),
inference(forward_demodulation,[],[f581,f453]) ).
fof(f581,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
| null_class = intersection(cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class),X1)
| subclass(X0,domain_of(X1)) )
| ~ spl0_28
| ~ spl0_70 ),
inference(resolution,[],[f569,f324]) ).
fof(f1580,plain,
( spl0_186
| ~ spl0_77
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f680,f677,f613,f1578]) ).
fof(f680,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
| ~ member(compose(X1,X0),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_77
| ~ spl0_88 ),
inference(resolution,[],[f678,f614]) ).
fof(f1558,plain,
( spl0_185
| ~ spl0_49
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f617,f608,f448,f1556]) ).
fof(f617,plain,
( ! [X0] :
( member(X0,subset_relation)
| ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,cross_product(universal_class,universal_class)) )
| ~ spl0_49
| ~ spl0_76 ),
inference(superposition,[],[f449,f610]) ).
fof(f1551,plain,
( spl0_184
| ~ spl0_38
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f622,f613,f372,f1549]) ).
fof(f622,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| ~ subclass(cross_product(X3,X1),X4)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) )
| ~ spl0_38
| ~ spl0_77 ),
inference(resolution,[],[f614,f373]) ).
fof(f1545,plain,
( ~ spl0_181
| ~ spl0_182
| spl0_183
| ~ spl0_22
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f606,f596,f295,f1542,f1538,f1534]) ).
fof(f1534,plain,
( spl0_181
<=> function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1542,plain,
( spl0_183
<=> inductive(cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f596,plain,
( spl0_75
<=> ! [X0] :
( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| inductive(X0)
| ~ member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f606,plain,
( inductive(cross_product(universal_class,universal_class))
| ~ member(null_class,cross_product(universal_class,universal_class))
| ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class)))))
| ~ spl0_22
| ~ spl0_75 ),
inference(resolution,[],[f597,f296]) ).
fof(f597,plain,
( ! [X0] :
( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| inductive(X0)
| ~ member(null_class,X0) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f596]) ).
fof(f1532,plain,
( spl0_180
| ~ spl0_39
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f514,f503,f376,f1530]) ).
fof(f1530,plain,
( spl0_180
<=> ! [X0] :
( ~ operation(X0)
| ~ subclass(domain_of(domain_of(X0)),domain_of(domain_of(flip(cross_product(X0,universal_class)))))
| domain_of(domain_of(flip(cross_product(X0,universal_class)))) = domain_of(domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f514,plain,
( ! [X0] :
( ~ operation(X0)
| ~ subclass(domain_of(domain_of(X0)),domain_of(domain_of(flip(cross_product(X0,universal_class)))))
| domain_of(domain_of(flip(cross_product(X0,universal_class)))) = domain_of(domain_of(X0)) )
| ~ spl0_39
| ~ spl0_57 ),
inference(resolution,[],[f504,f377]) ).
fof(f1525,plain,
( spl0_178
| spl0_179
| ~ spl0_40
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f601,f588,f380,f1522,f1519]) ).
fof(f1519,plain,
( spl0_178
<=> ! [X0] :
( ~ member(X0,universal_class)
| null_class = cross_product(X0,universal_class)
| ~ function(regular(cross_product(X0,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f601,plain,
( ! [X0] :
( member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
| ~ member(X0,universal_class)
| ~ function(regular(cross_product(X0,universal_class)))
| null_class = cross_product(X0,universal_class) )
| ~ spl0_40
| ~ spl0_73 ),
inference(superposition,[],[f589,f381]) ).
fof(f1517,plain,
( spl0_177
| ~ spl0_63
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f547,f543,f532,f1515]) ).
fof(f1515,plain,
( spl0_177
<=> ! [X0] :
( ~ function(intersection(successor_relation,cross_product(X0,universal_class)))
| maps(intersection(successor_relation,cross_product(X0,universal_class)),domain_of(intersection(successor_relation,cross_product(X0,universal_class))),X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f543,plain,
( spl0_65
<=> ! [X1,X8] :
( ~ function(X8)
| ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
| maps(X8,domain_of(X8),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f547,plain,
( ! [X0] :
( ~ function(intersection(successor_relation,cross_product(X0,universal_class)))
| maps(intersection(successor_relation,cross_product(X0,universal_class)),domain_of(intersection(successor_relation,cross_product(X0,universal_class))),X0)
| ~ inductive(X0) )
| ~ spl0_63
| ~ spl0_65 ),
inference(resolution,[],[f544,f533]) ).
fof(f544,plain,
( ! [X1,X8] :
( ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
| ~ function(X8)
| maps(X8,domain_of(X8),X1) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f1479,plain,
( spl0_176
| ~ spl0_77
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f667,f664,f613,f1477]) ).
fof(f667,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_77
| ~ spl0_85 ),
inference(resolution,[],[f665,f614]) ).
fof(f1475,plain,
( ~ spl0_174
| spl0_175
| ~ spl0_14
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f913,f892,f262,f1472,f1468]) ).
fof(f1468,plain,
( spl0_174
<=> single_valued_class(domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1472,plain,
( spl0_175
<=> function(domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f913,plain,
( function(domain_relation)
| ~ single_valued_class(domain_relation)
| ~ spl0_14
| ~ spl0_114 ),
inference(resolution,[],[f893,f264]) ).
fof(f1466,plain,
( spl0_172
| spl0_173
| ~ spl0_12
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f632,f628,f254,f1463,f1460]) ).
fof(f1460,plain,
( spl0_172
<=> ! [X0,X1] : ~ inductive(cross_product(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f1463,plain,
( spl0_173
<=> null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f632,plain,
( ! [X0,X1] :
( null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))))
| ~ inductive(cross_product(X0,X1)) )
| ~ spl0_12
| ~ spl0_79 ),
inference(resolution,[],[f629,f255]) ).
fof(f1458,plain,
( spl0_171
| ~ spl0_38
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f603,f592,f372,f1456]) ).
fof(f592,plain,
( spl0_74
<=> ! [X2] :
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f603,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(universal_class,X1)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1) )
| ~ spl0_38
| ~ spl0_74 ),
inference(resolution,[],[f593,f373]) ).
fof(f593,plain,
( ! [X2] :
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
| ~ member(X2,universal_class) )
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f1454,plain,
( spl0_170
| ~ spl0_38
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f599,f588,f372,f1452]) ).
fof(f599,plain,
( ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ function(X1)
| ~ subclass(universal_class,X2)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2) )
| ~ spl0_38
| ~ spl0_73 ),
inference(resolution,[],[f589,f373]) ).
fof(f1450,plain,
( spl0_169
| ~ spl0_39
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f494,f460,f376,f1448]) ).
fof(f1448,plain,
( spl0_169
<=> ! [X0] :
( ~ function(X0)
| ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f494,plain,
( ! [X0] :
( ~ function(X0)
| ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) )
| ~ spl0_39
| ~ spl0_52 ),
inference(resolution,[],[f461,f377]) ).
fof(f1446,plain,
( spl0_168
| ~ spl0_39
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f493,f456,f376,f1444]) ).
fof(f1444,plain,
( spl0_168
<=> ! [X0] :
( ~ single_valued_class(X0)
| ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f493,plain,
( ! [X0] :
( ~ single_valued_class(X0)
| ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) )
| ~ spl0_39
| ~ spl0_51 ),
inference(resolution,[],[f457,f377]) ).
fof(f1379,plain,
( spl0_167
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f648,f645,f1377]) ).
fof(f645,plain,
( spl0_82
<=> ! [X9,X11,X10] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f648,plain,
( ! [X0,X1] :
( compatible(domain_of(X0),X0,X1)
| ~ function(domain_of(X0))
| ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1))) )
| ~ spl0_82 ),
inference(equality_resolution,[],[f646]) ).
fof(f646,plain,
( ! [X10,X11,X9] :
( domain_of(domain_of(X10)) != domain_of(X9)
| compatible(X9,X10,X11)
| ~ function(X9)
| ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) )
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f645]) ).
fof(f1375,plain,
( spl0_166
| ~ spl0_38
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f580,f568,f372,f1373]) ).
fof(f580,plain,
( ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
| ~ subclass(domain_of(X1),X2)
| member(X0,X2) )
| ~ spl0_38
| ~ spl0_70 ),
inference(resolution,[],[f569,f373]) ).
fof(f1371,plain,
( spl0_165
| ~ spl0_38
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f572,f552,f372,f1369]) ).
fof(f572,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(domain_relation,X1)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1) )
| ~ spl0_38
| ~ spl0_66 ),
inference(resolution,[],[f553,f373]) ).
fof(f1367,plain,
( spl0_164
| ~ spl0_28
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f483,f448,f323,f1365]) ).
fof(f483,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
| ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2)) )
| ~ spl0_28
| ~ spl0_49 ),
inference(resolution,[],[f449,f324]) ).
fof(f1363,plain,
( spl0_163
| ~ spl0_27
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f475,f444,f319,f1361]) ).
fof(f475,plain,
( ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X0
| not_subclass_element(unordered_pair(X0,X1),X2) = X1
| subclass(unordered_pair(X0,X1),X2) )
| ~ spl0_27
| ~ spl0_48 ),
inference(resolution,[],[f445,f320]) ).
fof(f1353,plain,
( spl0_162
| ~ spl0_32
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f618,f608,f339,f1351]) ).
fof(f618,plain,
( ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
| ~ spl0_32
| ~ spl0_76 ),
inference(superposition,[],[f340,f610]) ).
fof(f1322,plain,
( spl0_161
| ~ spl0_50
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f600,f588,f452,f1320]) ).
fof(f600,plain,
( ! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ member(X0,universal_class)
| ~ function(X1) )
| ~ spl0_50
| ~ spl0_73 ),
inference(superposition,[],[f589,f453]) ).
fof(f1318,plain,
( spl0_160
| ~ spl0_23
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f474,f444,f299,f1316]) ).
fof(f474,plain,
( ! [X0,X1] :
( regular(unordered_pair(X0,X1)) = X0
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class )
| ~ spl0_23
| ~ spl0_48 ),
inference(resolution,[],[f445,f300]) ).
fof(f1300,plain,
( spl0_159
| ~ spl0_22
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f550,f543,f295,f1298]) ).
fof(f1298,plain,
( spl0_159
<=> ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),cross_product(universal_class,universal_class))
| ~ function(domain_of(domain_of(flip(cross_product(X0,universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f550,plain,
( ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),cross_product(universal_class,universal_class))
| ~ function(domain_of(domain_of(flip(cross_product(X0,universal_class))))) )
| ~ spl0_22
| ~ spl0_65 ),
inference(resolution,[],[f544,f296]) ).
fof(f1296,plain,
( spl0_158
| ~ spl0_40
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f522,f516,f380,f1294]) ).
fof(f516,plain,
( spl0_60
<=> ! [X4,X0] :
( ~ member(X4,domain_of(X0))
| null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f522,plain,
( ! [X0] :
( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_40
| ~ spl0_60 ),
inference(trivial_inequality_removal,[],[f520]) ).
fof(f520,plain,
( ! [X0] :
( null_class != null_class
| ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
| null_class = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_40
| ~ spl0_60 ),
inference(superposition,[],[f517,f381]) ).
fof(f517,plain,
( ! [X0,X4] :
( null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0)
| ~ member(X4,domain_of(X0)) )
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f1292,plain,
( spl0_157
| ~ spl0_28
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f437,f424,f323,f1290]) ).
fof(f437,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| ~ member(not_subclass_element(X0,complement(X1)),universal_class)
| subclass(X0,complement(X1)) )
| ~ spl0_28
| ~ spl0_44 ),
inference(resolution,[],[f425,f324]) ).
fof(f1288,plain,
( ~ spl0_155
| spl0_156
| ~ spl0_11
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f909,f892,f249,f1285,f1281]) ).
fof(f1281,plain,
( spl0_155
<=> single_valued_class(successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1285,plain,
( spl0_156
<=> function(successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f909,plain,
( function(successor_relation)
| ~ single_valued_class(successor_relation)
| ~ spl0_11
| ~ spl0_114 ),
inference(resolution,[],[f893,f251]) ).
fof(f1279,plain,
( spl0_154
| ~ spl0_34
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f409,f376,f347,f1277]) ).
fof(f409,plain,
( ! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
| cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
| ~ spl0_34
| ~ spl0_39 ),
inference(resolution,[],[f377,f348]) ).
fof(f1275,plain,
( spl0_153
| ~ spl0_33
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f408,f376,f343,f1273]) ).
fof(f408,plain,
( ! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
| rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) )
| ~ spl0_33
| ~ spl0_39 ),
inference(resolution,[],[f377,f344]) ).
fof(f1249,plain,
( spl0_152
| ~ spl0_38
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f497,f468,f372,f1247]) ).
fof(f468,plain,
( spl0_54
<=> ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f497,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(universal_class,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) )
| ~ spl0_38
| ~ spl0_54 ),
inference(resolution,[],[f469,f373]) ).
fof(f469,plain,
( ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f1245,plain,
( spl0_151
| ~ spl0_38
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f482,f448,f372,f1243]) ).
fof(f482,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| ~ subclass(intersection(X2,X1),X3)
| member(X0,X3) )
| ~ spl0_38
| ~ spl0_49 ),
inference(resolution,[],[f449,f373]) ).
fof(f1241,plain,
( spl0_149
| ~ spl0_150
| ~ spl0_25
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f416,f376,f308,f1238,f1234]) ).
fof(f1234,plain,
( spl0_149
<=> cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f416,plain,
( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
| cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function
| ~ spl0_25
| ~ spl0_39 ),
inference(resolution,[],[f377,f310]) ).
fof(f1232,plain,
( spl0_147
| ~ spl0_148
| ~ spl0_24
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f414,f376,f303,f1229,f1225]) ).
fof(f1225,plain,
( spl0_147
<=> composition_function = cross_product(universal_class,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f414,plain,
( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
| composition_function = cross_product(universal_class,cross_product(universal_class,universal_class))
| ~ spl0_24
| ~ spl0_39 ),
inference(resolution,[],[f377,f305]) ).
fof(f1223,plain,
( spl0_146
| ~ spl0_21
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f412,f376,f291,f1221]) ).
fof(f412,plain,
( ! [X0,X1] :
( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
| cross_product(universal_class,universal_class) = compose(X0,X1) )
| ~ spl0_21
| ~ spl0_39 ),
inference(resolution,[],[f377,f292]) ).
fof(f1173,plain,
( spl0_145
| ~ spl0_50
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f519,f516,f452,f1171]) ).
fof(f519,plain,
( ! [X0,X1] :
( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,domain_of(X1)) )
| ~ spl0_50
| ~ spl0_60 ),
inference(superposition,[],[f517,f453]) ).
fof(f1169,plain,
( spl0_144
| ~ spl0_43
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f486,f448,f393,f1167]) ).
fof(f486,plain,
( ! [X0] :
( member(X0,identity_relation)
| ~ member(X0,subset_relation)
| ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_43
| ~ spl0_49 ),
inference(superposition,[],[f449,f395]) ).
fof(f1165,plain,
( spl0_143
| ~ spl0_41
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f485,f448,f384,f1163]) ).
fof(f485,plain,
( ! [X0] :
( member(X0,singleton_relation)
| ~ member(X0,element_relation)
| ~ member(X0,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_41
| ~ spl0_49 ),
inference(superposition,[],[f449,f386]) ).
fof(f1161,plain,
( spl0_142
| ~ spl0_40
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f484,f448,f380,f1159]) ).
fof(f484,plain,
( ! [X0,X1] :
( member(X1,null_class)
| ~ member(X1,regular(X0))
| ~ member(X1,X0)
| null_class = X0 )
| ~ spl0_40
| ~ spl0_49 ),
inference(superposition,[],[f449,f381]) ).
fof(f1157,plain,
( spl0_141
| ~ spl0_38
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f436,f424,f372,f1155]) ).
fof(f436,plain,
( ! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,universal_class)
| ~ subclass(complement(X1),X2)
| member(X0,X2) )
| ~ spl0_38
| ~ spl0_44 ),
inference(resolution,[],[f425,f373]) ).
fof(f1110,plain,
( spl0_140
| ~ spl0_6
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f549,f543,f228,f1108]) ).
fof(f1108,plain,
( spl0_140
<=> ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),domain_of(domain_of(flip(cross_product(X0,universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f549,plain,
( ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),domain_of(domain_of(flip(cross_product(X0,universal_class))))) )
| ~ spl0_6
| ~ spl0_65 ),
inference(resolution,[],[f544,f229]) ).
fof(f1106,plain,
( ~ spl0_138
| spl0_139
| ~ spl0_10
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f907,f892,f244,f1103,f1099]) ).
fof(f1099,plain,
( spl0_138
<=> single_valued_class(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1103,plain,
( spl0_139
<=> function(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f244,plain,
( spl0_10
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f907,plain,
( function(element_relation)
| ~ single_valued_class(element_relation)
| ~ spl0_10
| ~ spl0_114 ),
inference(resolution,[],[f893,f246]) ).
fof(f246,plain,
( subclass(element_relation,cross_product(universal_class,universal_class))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f1097,plain,
( spl0_137
| ~ spl0_18
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f413,f376,f279,f1095]) ).
fof(f413,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
| cross_product(universal_class,universal_class) = compose_class(X0) )
| ~ spl0_18
| ~ spl0_39 ),
inference(resolution,[],[f377,f280]) ).
fof(f1093,plain,
( spl0_136
| ~ spl0_22
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f406,f376,f295,f1091]) ).
fof(f406,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| cross_product(universal_class,universal_class) = X0
| ~ function(X0) )
| ~ spl0_22
| ~ spl0_39 ),
inference(resolution,[],[f377,f296]) ).
fof(f1089,plain,
( spl0_135
| ~ spl0_27
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f370,f339,f319,f1087]) ).
fof(f370,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) )
| ~ spl0_27
| ~ spl0_32 ),
inference(resolution,[],[f340,f320]) ).
fof(f1085,plain,
( spl0_134
| ~ spl0_27
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f367,f335,f319,f1083]) ).
fof(f367,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) )
| ~ spl0_27
| ~ spl0_31 ),
inference(resolution,[],[f336,f320]) ).
fof(f1026,plain,
( spl0_133
| ~ spl0_57
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f546,f543,f503,f1024]) ).
fof(f1024,plain,
( spl0_133
<=> ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),domain_of(domain_of(X0)))
| ~ operation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f546,plain,
( ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),domain_of(domain_of(X0)))
| ~ operation(X0) )
| ~ spl0_57
| ~ spl0_65 ),
inference(resolution,[],[f544,f504]) ).
fof(f1022,plain,
( spl0_132
| ~ spl0_30
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f403,f372,f331,f1020]) ).
fof(f403,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X1,X2)
| ~ member(X1,universal_class) )
| ~ spl0_30
| ~ spl0_38 ),
inference(resolution,[],[f373,f332]) ).
fof(f1018,plain,
( spl0_131
| ~ spl0_29
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f402,f372,f327,f1016]) ).
fof(f402,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,universal_class) )
| ~ spl0_29
| ~ spl0_38 ),
inference(resolution,[],[f373,f328]) ).
fof(f1014,plain,
( spl0_130
| ~ spl0_27
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f401,f372,f319,f1012]) ).
fof(f401,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| member(not_subclass_element(X0,X2),X1)
| subclass(X0,X2) )
| ~ spl0_27
| ~ spl0_38 ),
inference(resolution,[],[f373,f320]) ).
fof(f1010,plain,
( spl0_129
| ~ spl0_23
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f369,f339,f299,f1008]) ).
fof(f369,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),X1)
| intersection(X0,X1) = null_class )
| ~ spl0_23
| ~ spl0_32 ),
inference(resolution,[],[f340,f300]) ).
fof(f1006,plain,
( spl0_128
| ~ spl0_23
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f366,f335,f299,f1004]) ).
fof(f366,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),X0)
| intersection(X0,X1) = null_class )
| ~ spl0_23
| ~ spl0_31 ),
inference(resolution,[],[f336,f300]) ).
fof(f987,plain,
( ~ spl0_127
| ~ spl0_12
| spl0_108 ),
inference(avatar_split_clause,[],[f940,f810,f254,f984]) ).
fof(f984,plain,
( spl0_127
<=> inductive(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f810,plain,
( spl0_108
<=> member(null_class,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f940,plain,
( ~ inductive(element_relation)
| ~ spl0_12
| spl0_108 ),
inference(resolution,[],[f811,f255]) ).
fof(f811,plain,
( ~ member(null_class,element_relation)
| spl0_108 ),
inference(avatar_component_clause,[],[f810]) ).
fof(f965,plain,
( spl0_126
| ~ spl0_12
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f473,f444,f254,f963]) ).
fof(f473,plain,
( ! [X0,X1] :
( null_class = X0
| null_class = X1
| ~ inductive(unordered_pair(X0,X1)) )
| ~ spl0_12
| ~ spl0_48 ),
inference(resolution,[],[f445,f255]) ).
fof(f961,plain,
( spl0_125
| ~ spl0_31
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f422,f393,f335,f959]) ).
fof(f422,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_31
| ~ spl0_43 ),
inference(superposition,[],[f336,f395]) ).
fof(f957,plain,
( spl0_124
| ~ spl0_31
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f420,f384,f335,f955]) ).
fof(f420,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_31
| ~ spl0_41 ),
inference(superposition,[],[f336,f386]) ).
fof(f953,plain,
( spl0_123
| ~ spl0_32
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f417,f380,f339,f951]) ).
fof(f417,plain,
( ! [X0,X1] :
( ~ member(X1,null_class)
| member(X1,regular(X0))
| null_class = X0 )
| ~ spl0_32
| ~ spl0_40 ),
inference(superposition,[],[f340,f381]) ).
fof(f949,plain,
( spl0_121
| ~ spl0_122
| ~ spl0_14
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f415,f376,f262,f946,f942]) ).
fof(f942,plain,
( spl0_121
<=> cross_product(universal_class,universal_class) = domain_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f415,plain,
( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
| cross_product(universal_class,universal_class) = domain_relation
| ~ spl0_14
| ~ spl0_39 ),
inference(resolution,[],[f377,f264]) ).
fof(f939,plain,
( spl0_119
| ~ spl0_120
| ~ spl0_11
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f410,f376,f249,f936,f932]) ).
fof(f932,plain,
( spl0_119
<=> cross_product(universal_class,universal_class) = successor_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f410,plain,
( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
| cross_product(universal_class,universal_class) = successor_relation
| ~ spl0_11
| ~ spl0_39 ),
inference(resolution,[],[f377,f251]) ).
fof(f930,plain,
( spl0_117
| ~ spl0_118
| ~ spl0_10
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f407,f376,f244,f927,f923]) ).
fof(f923,plain,
( spl0_117
<=> element_relation = cross_product(universal_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f407,plain,
( ~ subclass(cross_product(universal_class,universal_class),element_relation)
| element_relation = cross_product(universal_class,universal_class)
| ~ spl0_10
| ~ spl0_39 ),
inference(resolution,[],[f377,f246]) ).
fof(f921,plain,
( spl0_116
| ~ spl0_23
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f400,f372,f299,f919]) ).
fof(f400,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| member(regular(X0),X1)
| null_class = X0 )
| ~ spl0_23
| ~ spl0_38 ),
inference(resolution,[],[f373,f300]) ).
fof(f917,plain,
( spl0_115
| ~ spl0_20
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f362,f319,f287,f915]) ).
fof(f362,plain,
( ! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) )
| ~ spl0_20
| ~ spl0_27 ),
inference(resolution,[],[f320,f288]) ).
fof(f894,plain,
( spl0_114
| ~ spl0_51
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f579,f564,f456,f892]) ).
fof(f564,plain,
( spl0_69
<=> ! [X8] :
( function(X8)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f579,plain,
( ! [X0] :
( ~ subclass(X0,cross_product(universal_class,universal_class))
| function(X0)
| ~ single_valued_class(X0) )
| ~ spl0_51
| ~ spl0_69 ),
inference(resolution,[],[f565,f457]) ).
fof(f565,plain,
( ! [X8] :
( ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| function(X8) )
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f564]) ).
fof(f890,plain,
( spl0_113
| ~ spl0_31
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f418,f380,f335,f888]) ).
fof(f418,plain,
( ! [X0,X1] :
( ~ member(X1,null_class)
| member(X1,X0)
| null_class = X0 )
| ~ spl0_31
| ~ spl0_40 ),
inference(superposition,[],[f336,f381]) ).
fof(f886,plain,
( spl0_112
| ~ spl0_20
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f317,f299,f287,f884]) ).
fof(f317,plain,
( ! [X0] :
( complement(X0) = null_class
| ~ member(regular(complement(X0)),X0) )
| ~ spl0_20
| ~ spl0_23 ),
inference(resolution,[],[f300,f288]) ).
fof(f825,plain,
( spl0_111
| ~ spl0_31
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f619,f608,f335,f823]) ).
fof(f619,plain,
( ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,cross_product(universal_class,universal_class)) )
| ~ spl0_31
| ~ spl0_76 ),
inference(superposition,[],[f336,f610]) ).
fof(f821,plain,
( spl0_110
| ~ spl0_13
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f411,f376,f258,f819]) ).
fof(f411,plain,
( ! [X0] :
( ~ subclass(X0,omega)
| omega = X0
| ~ inductive(X0) )
| ~ spl0_13
| ~ spl0_39 ),
inference(resolution,[],[f377,f259]) ).
fof(f817,plain,
( spl0_109
| ~ spl0_12
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f399,f372,f254,f815]) ).
fof(f399,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| member(null_class,X1)
| ~ inductive(X0) )
| ~ spl0_12
| ~ spl0_38 ),
inference(resolution,[],[f373,f255]) ).
fof(f813,plain,
( ~ spl0_107
| spl0_108
| ~ spl0_12
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f771,f731,f254,f810,f806]) ).
fof(f806,plain,
( spl0_107
<=> inductive(singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f771,plain,
( member(null_class,element_relation)
| ~ inductive(singleton_relation)
| ~ spl0_12
| ~ spl0_97 ),
inference(resolution,[],[f732,f255]) ).
fof(f804,plain,
( spl0_106
| ~ spl0_9
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f398,f372,f240,f802]) ).
fof(f398,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| member(unordered_pair(X1,X2),X0) )
| ~ spl0_9
| ~ spl0_38 ),
inference(resolution,[],[f373,f241]) ).
fof(f791,plain,
( spl0_105
| ~ spl0_4
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f548,f543,f219,f789]) ).
fof(f789,plain,
( spl0_105
<=> ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f548,plain,
( ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),universal_class) )
| ~ spl0_4
| ~ spl0_65 ),
inference(resolution,[],[f544,f220]) ).
fof(f781,plain,
( spl0_104
| ~ spl0_12
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f368,f339,f254,f779]) ).
fof(f779,plain,
( spl0_104
<=> ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f368,plain,
( ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X1,X0)) )
| ~ spl0_12
| ~ spl0_32 ),
inference(resolution,[],[f340,f255]) ).
fof(f763,plain,
( spl0_103
| ~ spl0_32
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f421,f393,f339,f761]) ).
fof(f421,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) )
| ~ spl0_32
| ~ spl0_43 ),
inference(superposition,[],[f340,f395]) ).
fof(f759,plain,
spl0_102,
inference(avatar_split_clause,[],[f202,f757]) ).
fof(f757,plain,
( spl0_102
<=> ! [X9,X11,X10] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f202,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f201,f128]) ).
fof(f128,plain,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5),
inference(definition_unfolding,[],[f28,f29]) ).
fof(f29,axiom,
! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction2) ).
fof(f28,axiom,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction1) ).
fof(f201,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f200,f128]) ).
fof(f200,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f199,f128]) ).
fof(f199,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f198,f128]) ).
fof(f198,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f197,f128]) ).
fof(f197,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f196,f128]) ).
fof(f196,plain,
! [X10,X11,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f195,f128]) ).
fof(f195,plain,
! [X10,X11,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class)))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f194,f128]) ).
fof(f194,plain,
! [X10,X11,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f193,f128]) ).
fof(f193,plain,
! [X10,X11,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f175,f128]) ).
fof(f175,plain,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
inference(definition_unfolding,[],[f91,f117,f118,f117,f117,f117,f117,f118]) ).
fof(f118,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f117,plain,
! [X1,X8] : apply(X8,X1) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X8),universal_class))))),element_relation)),
inference(definition_unfolding,[],[f68,f114,f116,f12]) ).
fof(f116,plain,
! [X0,X5] : image(X5,X0) = domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X5),universal_class)))),
inference(definition_unfolding,[],[f42,f115,f29]) ).
fof(f115,plain,
! [X4] : range_of(X4) = domain_of(domain_of(flip(cross_product(X4,universal_class)))),
inference(definition_unfolding,[],[f39,f38]) ).
fof(f38,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f39,axiom,
! [X4] : domain_of(inverse(X4)) = range_of(X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of) ).
fof(f42,axiom,
! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image) ).
fof(f114,plain,
! [X0] : sum_class(X0) = domain_of(intersection(cross_product(universal_class,X0),element_relation)),
inference(definition_unfolding,[],[f53,f29]) ).
fof(f53,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_definition) ).
fof(f68,axiom,
! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply) ).
fof(f91,axiom,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| apply(X11,ordered_pair(apply(X9,not_homomorphism1(X9,X10,X11)),apply(X9,not_homomorphism2(X9,X10,X11)))) != apply(X9,apply(X10,ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism6) ).
fof(f752,plain,
spl0_101,
inference(avatar_split_clause,[],[f192,f750]) ).
fof(f192,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
inference(forward_demodulation,[],[f191,f128]) ).
fof(f191,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
inference(forward_demodulation,[],[f190,f128]) ).
fof(f190,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
inference(forward_demodulation,[],[f189,f128]) ).
fof(f189,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
inference(forward_demodulation,[],[f188,f128]) ).
fof(f188,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
inference(forward_demodulation,[],[f167,f128]) ).
fof(f167,plain,
! [X10,X0,X11,X1,X9] :
( ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10))
| domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
inference(definition_unfolding,[],[f89,f118,f117,f118,f117,f117,f117,f117,f118]) ).
fof(f89,axiom,
! [X10,X0,X11,X1,X9] :
( ~ homomorphism(X9,X10,X11)
| ~ member(ordered_pair(X0,X1),domain_of(X10))
| apply(X11,ordered_pair(apply(X9,X0),apply(X9,X1))) = apply(X9,apply(X10,ordered_pair(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism4) ).
fof(f747,plain,
spl0_100,
inference(avatar_split_clause,[],[f187,f745]) ).
fof(f187,plain,
! [X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(X1,domain_of(X0))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
inference(forward_demodulation,[],[f166,f128]) ).
fof(f166,plain,
! [X0,X1,X4] :
( ~ member(X1,domain_of(X0))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)))))))),application_function)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
inference(definition_unfolding,[],[f108,f118,f118,f117,f118,f118]) ).
fof(f108,axiom,
! [X0,X1,X4] :
( ~ member(X1,domain_of(X0))
| member(ordered_pair(X0,ordered_pair(X1,apply(X0,X1))),application_function)
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn4) ).
fof(f741,plain,
spl0_99,
inference(avatar_split_clause,[],[f171,f739]) ).
fof(f171,plain,
! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(definition_unfolding,[],[f37,f118,f118,f118,f118,f118,f118]) ).
fof(f37,axiom,
! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X3,X2),X6),X0)
| member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip3) ).
fof(f737,plain,
spl0_98,
inference(avatar_split_clause,[],[f170,f735]) ).
fof(f170,plain,
! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(definition_unfolding,[],[f34,f118,f118,f118,f118,f118,f118]) ).
fof(f34,axiom,
! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X3,X6),X2),X0)
| member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate3) ).
fof(f733,plain,
( spl0_97
| ~ spl0_32
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f419,f384,f339,f731]) ).
fof(f419,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,element_relation) )
| ~ spl0_32
| ~ spl0_41 ),
inference(superposition,[],[f340,f386]) ).
fof(f729,plain,
spl0_96,
inference(avatar_split_clause,[],[f155,f727]) ).
fof(f155,plain,
! [X2,X3,X0,X6] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ),
inference(definition_unfolding,[],[f36,f118,f118,f118,f118]) ).
fof(f36,axiom,
! [X2,X3,X0,X6] :
( member(ordered_pair(ordered_pair(X3,X2),X6),X0)
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip2) ).
fof(f725,plain,
spl0_95,
inference(avatar_split_clause,[],[f154,f723]) ).
fof(f154,plain,
! [X2,X3,X0,X6] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ),
inference(definition_unfolding,[],[f33,f118,f118,f118,f118]) ).
fof(f33,axiom,
! [X2,X3,X0,X6] :
( member(ordered_pair(ordered_pair(X3,X6),X2),X0)
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate2) ).
fof(f720,plain,
spl0_94,
inference(avatar_split_clause,[],[f178,f718]) ).
fof(f178,plain,
! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ),
inference(equality_resolution,[],[f165]) ).
fof(f165,plain,
! [X0,X1] :
( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) != X1
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f46,f124,f118,f118]) ).
fof(f124,plain,
! [X0] : successor(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),
inference(definition_unfolding,[],[f43,f26,f12]) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f43,axiom,
! [X0] : union(X0,singleton(X0)) = successor(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor) ).
fof(f46,axiom,
! [X0,X1] :
( successor(X0) != X1
| member(ordered_pair(X0,X1),successor_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation3) ).
fof(f704,plain,
spl0_93,
inference(avatar_split_clause,[],[f169,f702]) ).
fof(f169,plain,
! [X1,X7,X4,X5] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
inference(definition_unfolding,[],[f59,f118,f118,f116,f116,f12]) ).
fof(f59,axiom,
! [X1,X7,X4,X5] :
( ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X4),compose(X7,X5))
| ~ member(X4,image(X7,image(X5,singleton(X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose3) ).
fof(f698,plain,
spl0_92,
inference(avatar_split_clause,[],[f152,f696]) ).
fof(f152,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function) ),
inference(definition_unfolding,[],[f97,f118,f118,f118]) ).
fof(f97,axiom,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| member(ordered_pair(X0,ordered_pair(X1,compose(X0,X1))),composition_function) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_composition_function3) ).
fof(f693,plain,
spl0_91,
inference(avatar_split_clause,[],[f183,f691]) ).
fof(f183,plain,
! [X0,X1,X4] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))) = X4
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
inference(forward_demodulation,[],[f149,f128]) ).
fof(f149,plain,
! [X0,X1,X4] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)) = X4
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
inference(definition_unfolding,[],[f107,f117,f118,f118]) ).
fof(f107,axiom,
! [X0,X1,X4] :
( apply(X0,X1) = X4
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn3) ).
fof(f688,plain,
spl0_90,
inference(avatar_split_clause,[],[f174,f686]) ).
fof(f174,plain,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10)) ),
inference(definition_unfolding,[],[f90,f118]) ).
fof(f90,axiom,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| member(ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)),domain_of(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism5) ).
fof(f684,plain,
spl0_89,
inference(avatar_split_clause,[],[f153,f682]) ).
fof(f153,plain,
! [X1,X7,X4,X5] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
inference(definition_unfolding,[],[f58,f118,f116,f116,f12]) ).
fof(f58,axiom,
! [X1,X7,X4,X5] :
( ~ member(ordered_pair(X1,X4),compose(X7,X5))
| member(X4,image(X7,image(X5,singleton(X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose2) ).
fof(f679,plain,
spl0_88,
inference(avatar_split_clause,[],[f179,f677]) ).
fof(f179,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class)) ),
inference(equality_resolution,[],[f168]) ).
fof(f168,plain,
! [X0,X1,X4] :
( compose(X0,X1) != X4
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f94,f118,f118]) ).
fof(f94,axiom,
! [X0,X1,X4] :
( compose(X0,X1) != X4
| member(ordered_pair(X1,X4),compose_class(X0))
| ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_class_definition3) ).
fof(f675,plain,
spl0_87,
inference(avatar_split_clause,[],[f151,f673]) ).
fof(f151,plain,
! [X0,X1,X4] :
( compose(X0,X1) = X4
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function) ),
inference(definition_unfolding,[],[f96,f118,f118]) ).
fof(f96,axiom,
! [X0,X1,X4] :
( compose(X0,X1) = X4
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),composition_function) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_composition_function2) ).
fof(f671,plain,
spl0_86,
inference(avatar_split_clause,[],[f147,f669]) ).
fof(f147,plain,
! [X0,X1,X4] :
( member(X1,domain_of(X0))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
inference(definition_unfolding,[],[f106,f118,f118]) ).
fof(f106,axiom,
! [X0,X1,X4] :
( member(X1,domain_of(X0))
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn2) ).
fof(f666,plain,
spl0_85,
inference(avatar_split_clause,[],[f162,f664]) ).
fof(f162,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f20,f118,f118]) ).
fof(f20,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| member(ordered_pair(X0,X1),element_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation3) ).
fof(f656,plain,
spl0_84,
inference(avatar_split_clause,[],[f186,f654]) ).
fof(f186,plain,
! [X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
| ~ member(X1,universal_class)
| null_class = X1 ),
inference(forward_demodulation,[],[f185,f128]) ).
fof(f185,plain,
! [X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),choice),universal_class))))))),X1)
| ~ member(X1,universal_class)
| null_class = X1 ),
inference(forward_demodulation,[],[f163,f128]) ).
fof(f163,plain,
! [X1] :
( ~ member(X1,universal_class)
| null_class = X1
| member(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),choice),universal_class))))),element_relation)),X1) ),
inference(definition_unfolding,[],[f70,f117]) ).
fof(f70,axiom,
! [X1] :
( ~ member(X1,universal_class)
| null_class = X1
| member(apply(choice,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice2) ).
fof(f652,plain,
spl0_83,
inference(avatar_split_clause,[],[f172,f650]) ).
fof(f650,plain,
( spl0_83
<=> ! [X8] :
( ~ function(X8)
| operation(X8)
| ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
| domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f172,plain,
! [X8] :
( ~ function(X8)
| operation(X8)
| ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
| domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
inference(definition_unfolding,[],[f81,f115]) ).
fof(f81,axiom,
! [X8] :
( ~ function(X8)
| operation(X8)
| ~ subclass(range_of(X8),domain_of(domain_of(X8)))
| domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation4) ).
fof(f647,plain,
spl0_82,
inference(avatar_split_clause,[],[f173,f645]) ).
fof(f173,plain,
! [X10,X11,X9] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
inference(definition_unfolding,[],[f85,f115]) ).
fof(f85,axiom,
! [X10,X11,X9] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(range_of(X9),domain_of(domain_of(X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible4) ).
fof(f643,plain,
( ~ spl0_80
| spl0_81
| ~ spl0_4
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f605,f596,f219,f640,f636]) ).
fof(f640,plain,
( spl0_81
<=> inductive(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f605,plain,
( inductive(universal_class)
| ~ member(null_class,universal_class)
| ~ spl0_4
| ~ spl0_75 ),
inference(resolution,[],[f597,f220]) ).
fof(f630,plain,
spl0_79,
inference(avatar_split_clause,[],[f148,f628]) ).
fof(f148,plain,
! [X0,X1,X4] :
( ~ member(X4,cross_product(X0,X1))
| unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ),
inference(definition_unfolding,[],[f17,f118]) ).
fof(f17,axiom,
! [X0,X1,X4] :
( ~ member(X4,cross_product(X0,X1))
| ordered_pair(first(X4),second(X4)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f626,plain,
spl0_78,
inference(avatar_split_clause,[],[f145,f624]) ).
fof(f145,plain,
! [X0,X1] :
( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(definition_unfolding,[],[f45,f124,f118]) ).
fof(f45,axiom,
! [X0,X1] :
( successor(X0) = X1
| ~ member(ordered_pair(X0,X1),successor_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation2) ).
fof(f615,plain,
spl0_77,
inference(avatar_split_clause,[],[f161,f613]) ).
fof(f161,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,X0)
| ~ member(X3,X1)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f16,f118]) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( ~ member(X2,X0)
| ~ member(X3,X1)
| member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f611,plain,
spl0_76,
inference(avatar_split_clause,[],[f129,f608]) ).
fof(f129,plain,
subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),
inference(definition_unfolding,[],[f74,f38]) ).
fof(f74,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_relation) ).
fof(f598,plain,
spl0_75,
inference(avatar_split_clause,[],[f184,f596]) ).
fof(f184,plain,
! [X0] :
( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| inductive(X0)
| ~ member(null_class,X0) ),
inference(forward_demodulation,[],[f159,f128]) ).
fof(f159,plain,
! [X0] :
( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
inference(definition_unfolding,[],[f49,f116]) ).
fof(f49,axiom,
! [X0] :
( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive3) ).
fof(f594,plain,
spl0_74,
inference(avatar_split_clause,[],[f181,f592]) ).
fof(f181,plain,
! [X2] :
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
| ~ member(X2,universal_class) ),
inference(forward_demodulation,[],[f136,f128]) ).
fof(f136,plain,
! [X2] :
( ~ member(X2,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X2),universal_class),element_relation),universal_class))))),universal_class) ),
inference(definition_unfolding,[],[f56,f125]) ).
fof(f125,plain,
! [X0] : power_class(X0) = complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X0),universal_class),element_relation),universal_class))))),
inference(definition_unfolding,[],[f55,f116]) ).
fof(f55,axiom,
! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_definition) ).
fof(f56,axiom,
! [X2] :
( ~ member(X2,universal_class)
| member(power_class(X2),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class2) ).
fof(f590,plain,
spl0_73,
inference(avatar_split_clause,[],[f157,f588]) ).
fof(f157,plain,
! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ),
inference(definition_unfolding,[],[f65,f116]) ).
fof(f65,axiom,
! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(image(X8,X0),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replacement) ).
fof(f586,plain,
spl0_72,
inference(avatar_split_clause,[],[f150,f584]) ).
fof(f150,plain,
! [X0,X1,X4] :
( compose(X0,X1) = X4
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0)) ),
inference(definition_unfolding,[],[f93,f118]) ).
fof(f93,axiom,
! [X0,X1,X4] :
( compose(X0,X1) = X4
| ~ member(ordered_pair(X1,X4),compose_class(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_class_definition2) ).
fof(f577,plain,
( spl0_71
| ~ spl0_3
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f536,f511,f214,f574]) ).
fof(f574,plain,
( spl0_71
<=> single_valued_class(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f536,plain,
( single_valued_class(choice)
| ~ spl0_3
| ~ spl0_59 ),
inference(resolution,[],[f512,f216]) ).
fof(f570,plain,
spl0_70,
inference(avatar_split_clause,[],[f164,f568]) ).
fof(f164,plain,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
inference(definition_unfolding,[],[f31,f29,f12]) ).
fof(f31,axiom,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f566,plain,
spl0_69,
inference(avatar_split_clause,[],[f160,f564]) ).
fof(f160,plain,
! [X8] :
( function(X8)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f64,f38]) ).
fof(f64,axiom,
! [X8] :
( function(X8)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,inverse(X8)),identity_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function3) ).
fof(f562,plain,
spl0_68,
inference(avatar_split_clause,[],[f141,f560]) ).
fof(f141,plain,
! [X2,X3,X0,X1] :
( member(X2,X0)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f14,f118]) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product1) ).
fof(f558,plain,
spl0_67,
inference(avatar_split_clause,[],[f140,f556]) ).
fof(f140,plain,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f15,f118]) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f554,plain,
spl0_66,
inference(avatar_split_clause,[],[f138,f552]) ).
fof(f138,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation) ),
inference(definition_unfolding,[],[f100,f118]) ).
fof(f100,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(ordered_pair(X0,domain_of(X0)),domain_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_domain_relation3) ).
fof(f545,plain,
spl0_65,
inference(avatar_split_clause,[],[f158,f543]) ).
fof(f158,plain,
! [X1,X8] :
( ~ function(X8)
| ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
| maps(X8,domain_of(X8),X1) ),
inference(definition_unfolding,[],[f112,f115]) ).
fof(f112,axiom,
! [X1,X8] :
( ~ function(X8)
| ~ subclass(range_of(X8),X1)
| maps(X8,domain_of(X8),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps4) ).
fof(f541,plain,
spl0_64,
inference(avatar_split_clause,[],[f146,f539]) ).
fof(f146,plain,
! [X0,X1] :
( domain_of(X0) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ),
inference(definition_unfolding,[],[f99,f118]) ).
fof(f99,axiom,
! [X0,X1] :
( domain_of(X0) = X1
| ~ member(ordered_pair(X0,X1),domain_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_domain_relation2) ).
fof(f534,plain,
spl0_63,
inference(avatar_split_clause,[],[f180,f532]) ).
fof(f180,plain,
! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ),
inference(forward_demodulation,[],[f132,f128]) ).
fof(f132,plain,
! [X0] :
( ~ inductive(X0)
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
inference(definition_unfolding,[],[f48,f116]) ).
fof(f48,axiom,
! [X0] :
( ~ inductive(X0)
| subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive2) ).
fof(f530,plain,
spl0_62,
inference(avatar_split_clause,[],[f144,f528]) ).
fof(f528,plain,
( spl0_62
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f144,plain,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
inference(definition_unfolding,[],[f84,f115]) ).
fof(f84,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| subclass(range_of(X9),domain_of(domain_of(X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible3) ).
fof(f526,plain,
spl0_61,
inference(avatar_split_clause,[],[f139,f524]) ).
fof(f139,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
inference(definition_unfolding,[],[f19,f118]) ).
fof(f19,axiom,
! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation2) ).
fof(f518,plain,
spl0_60,
inference(avatar_split_clause,[],[f142,f516]) ).
fof(f142,plain,
! [X0,X4] :
( ~ member(X4,domain_of(X0))
| null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
inference(definition_unfolding,[],[f30,f29,f12]) ).
fof(f30,axiom,
! [X0,X4] :
( ~ member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f513,plain,
( spl0_59
| ~ spl0_52
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f495,f464,f460,f511]) ).
fof(f464,plain,
( spl0_53
<=> ! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f495,plain,
( ! [X0] :
( single_valued_class(X0)
| ~ function(X0) )
| ~ spl0_52
| ~ spl0_53 ),
inference(resolution,[],[f465,f461]) ).
fof(f465,plain,
( ! [X0] :
( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| single_valued_class(X0) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f509,plain,
spl0_58,
inference(avatar_split_clause,[],[f143,f507]) ).
fof(f507,plain,
( spl0_58
<=> ! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f143,plain,
! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ),
inference(definition_unfolding,[],[f111,f115]) ).
fof(f111,axiom,
! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| subclass(range_of(X8),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps3) ).
fof(f505,plain,
spl0_57,
inference(avatar_split_clause,[],[f133,f503]) ).
fof(f133,plain,
! [X8] :
( ~ operation(X8)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
inference(definition_unfolding,[],[f80,f115]) ).
fof(f80,axiom,
! [X8] :
( ~ operation(X8)
| subclass(range_of(X8),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation3) ).
fof(f501,plain,
spl0_56,
inference(avatar_split_clause,[],[f79,f499]) ).
fof(f499,plain,
( spl0_56
<=> ! [X8] :
( ~ operation(X8)
| domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f79,axiom,
! [X8] :
( ~ operation(X8)
| domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation2) ).
fof(f479,plain,
( spl0_55
| ~ spl0_4
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f404,f376,f219,f477]) ).
fof(f404,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 )
| ~ spl0_4
| ~ spl0_39 ),
inference(resolution,[],[f377,f220]) ).
fof(f470,plain,
spl0_54,
inference(avatar_split_clause,[],[f182,f468]) ).
fof(f182,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ),
inference(forward_demodulation,[],[f137,f128]) ).
fof(f137,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
inference(definition_unfolding,[],[f54,f114]) ).
fof(f54,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(sum_class(X0),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class2) ).
fof(f466,plain,
spl0_53,
inference(avatar_split_clause,[],[f135,f464]) ).
fof(f135,plain,
! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f61,f38]) ).
fof(f61,axiom,
! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_class2) ).
fof(f462,plain,
spl0_52,
inference(avatar_split_clause,[],[f134,f460]) ).
fof(f134,plain,
! [X8] :
( ~ function(X8)
| subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f63,f38]) ).
fof(f63,axiom,
! [X8] :
( ~ function(X8)
| subclass(compose(X8,inverse(X8)),identity_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function2) ).
fof(f458,plain,
spl0_51,
inference(avatar_split_clause,[],[f130,f456]) ).
fof(f130,plain,
! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f60,f38]) ).
fof(f60,axiom,
! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,inverse(X0)),identity_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_class1) ).
fof(f454,plain,
spl0_50,
inference(avatar_split_clause,[],[f128,f452]) ).
fof(f450,plain,
spl0_49,
inference(avatar_split_clause,[],[f23,f448]) ).
fof(f23,axiom,
! [X0,X1,X4] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f446,plain,
spl0_48,
inference(avatar_split_clause,[],[f8,f444]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f441,plain,
( spl0_47
| ~ spl0_5
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f397,f372,f223,f439]) ).
fof(f223,plain,
( spl0_5
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f397,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(omega,X0) )
| ~ spl0_5
| ~ spl0_38 ),
inference(resolution,[],[f373,f225]) ).
fof(f225,plain,
( member(omega,universal_class)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f434,plain,
spl0_46,
inference(avatar_split_clause,[],[f156,f432]) ).
fof(f432,plain,
( spl0_46
<=> ! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f156,plain,
! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(domain_of(flip(cross_product(X8,universal_class)))) ),
inference(definition_unfolding,[],[f73,f38]) ).
fof(f73,axiom,
! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(inverse(X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one3) ).
fof(f430,plain,
spl0_45,
inference(avatar_split_clause,[],[f83,f428]) ).
fof(f428,plain,
( spl0_45
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f83,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible2) ).
fof(f426,plain,
spl0_44,
inference(avatar_split_clause,[],[f25,f424]) ).
fof(f25,axiom,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f396,plain,
spl0_43,
inference(avatar_split_clause,[],[f127,f393]) ).
fof(f127,plain,
identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),
inference(definition_unfolding,[],[f75,f38]) ).
fof(f75,axiom,
identity_relation = intersection(inverse(subset_relation),subset_relation),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation) ).
fof(f391,plain,
( spl0_42
| ~ spl0_12
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f365,f335,f254,f389]) ).
fof(f365,plain,
( ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X0,X1)) )
| ~ spl0_12
| ~ spl0_31 ),
inference(resolution,[],[f336,f255]) ).
fof(f387,plain,
spl0_41,
inference(avatar_split_clause,[],[f104,f384]) ).
fof(f104,axiom,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_can_define_singleton) ).
fof(f382,plain,
spl0_40,
inference(avatar_split_clause,[],[f67,f380]) ).
fof(f67,axiom,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
fof(f378,plain,
spl0_39,
inference(avatar_split_clause,[],[f7,f376]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f374,plain,
spl0_38,
inference(avatar_split_clause,[],[f1,f372]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f361,plain,
spl0_37,
inference(avatar_split_clause,[],[f131,f359]) ).
fof(f131,plain,
! [X8] :
( ~ one_to_one(X8)
| function(domain_of(flip(cross_product(X8,universal_class)))) ),
inference(definition_unfolding,[],[f72,f38]) ).
fof(f72,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(inverse(X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one2) ).
fof(f357,plain,
spl0_36,
inference(avatar_split_clause,[],[f110,f355]) ).
fof(f355,plain,
( spl0_36
<=> ! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| domain_of(X8) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f110,axiom,
! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| domain_of(X8) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps2) ).
fof(f353,plain,
spl0_35,
inference(avatar_split_clause,[],[f88,f351]) ).
fof(f351,plain,
( spl0_35
<=> ! [X9,X11,X10] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f88,axiom,
! [X10,X11,X9] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism3) ).
fof(f349,plain,
spl0_34,
inference(avatar_split_clause,[],[f35,f347]) ).
fof(f35,axiom,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip1) ).
fof(f345,plain,
spl0_33,
inference(avatar_split_clause,[],[f32,f343]) ).
fof(f32,axiom,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate1) ).
fof(f341,plain,
spl0_32,
inference(avatar_split_clause,[],[f22,f339]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f337,plain,
spl0_31,
inference(avatar_split_clause,[],[f21,f335]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f333,plain,
spl0_30,
inference(avatar_split_clause,[],[f10,f331]) ).
fof(f10,axiom,
! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f329,plain,
spl0_29,
inference(avatar_split_clause,[],[f9,f327]) ).
fof(f9,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f325,plain,
spl0_28,
inference(avatar_split_clause,[],[f3,f323]) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f321,plain,
spl0_27,
inference(avatar_split_clause,[],[f2,f319]) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f316,plain,
( spl0_26
| ~ spl0_12
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f312,f287,f254,f314]) ).
fof(f314,plain,
( spl0_26
<=> ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f312,plain,
( ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) )
| ~ spl0_12
| ~ spl0_20 ),
inference(resolution,[],[f288,f255]) ).
fof(f311,plain,
spl0_25,
inference(avatar_split_clause,[],[f105,f308]) ).
fof(f105,axiom,
subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn1) ).
fof(f306,plain,
spl0_24,
inference(avatar_split_clause,[],[f95,f303]) ).
fof(f95,axiom,
subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_composition_function1) ).
fof(f301,plain,
spl0_23,
inference(avatar_split_clause,[],[f66,f299]) ).
fof(f66,axiom,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
fof(f297,plain,
spl0_22,
inference(avatar_split_clause,[],[f62,f295]) ).
fof(f62,axiom,
! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).
fof(f293,plain,
spl0_21,
inference(avatar_split_clause,[],[f57,f291]) ).
fof(f57,axiom,
! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose1) ).
fof(f289,plain,
spl0_20,
inference(avatar_split_clause,[],[f24,f287]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f285,plain,
spl0_19,
inference(avatar_split_clause,[],[f109,f283]) ).
fof(f283,plain,
( spl0_19
<=> ! [X0,X1,X8] :
( function(X8)
| ~ maps(X8,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f109,axiom,
! [X0,X1,X8] :
( function(X8)
| ~ maps(X8,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps1) ).
fof(f281,plain,
spl0_18,
inference(avatar_split_clause,[],[f92,f279]) ).
fof(f92,axiom,
! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_class_definition1) ).
fof(f277,plain,
spl0_17,
inference(avatar_split_clause,[],[f87,f275]) ).
fof(f275,plain,
( spl0_17
<=> ! [X9,X11,X10] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f87,axiom,
! [X10,X11,X9] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).
fof(f273,plain,
spl0_16,
inference(avatar_split_clause,[],[f86,f271]) ).
fof(f271,plain,
( spl0_16
<=> ! [X9,X11,X10] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f86,axiom,
! [X10,X11,X9] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).
fof(f269,plain,
spl0_15,
inference(avatar_split_clause,[],[f82,f267]) ).
fof(f267,plain,
( spl0_15
<=> ! [X9,X11,X10] :
( function(X9)
| ~ compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f82,axiom,
! [X10,X11,X9] :
( function(X9)
| ~ compatible(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible1) ).
fof(f265,plain,
spl0_14,
inference(avatar_split_clause,[],[f98,f262]) ).
fof(f98,axiom,
subclass(domain_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_domain_relation1) ).
fof(f260,plain,
spl0_13,
inference(avatar_split_clause,[],[f51,f258]) ).
fof(f51,axiom,
! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive2) ).
fof(f256,plain,
spl0_12,
inference(avatar_split_clause,[],[f47,f254]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).
fof(f252,plain,
spl0_11,
inference(avatar_split_clause,[],[f44,f249]) ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation1) ).
fof(f247,plain,
spl0_10,
inference(avatar_split_clause,[],[f18,f244]) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).
fof(f242,plain,
spl0_9,
inference(avatar_split_clause,[],[f11,f240]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f238,plain,
spl0_8,
inference(avatar_split_clause,[],[f78,f236]) ).
fof(f236,plain,
( spl0_8
<=> ! [X8] :
( ~ operation(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f78,axiom,
! [X8] :
( ~ operation(X8)
| function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation1) ).
fof(f234,plain,
spl0_7,
inference(avatar_split_clause,[],[f71,f232]) ).
fof(f232,plain,
( spl0_7
<=> ! [X8] :
( ~ one_to_one(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f71,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one1) ).
fof(f230,plain,
spl0_6,
inference(avatar_split_clause,[],[f176,f228]) ).
fof(f176,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( X0 != X1
| subclass(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass2) ).
fof(f226,plain,
spl0_5,
inference(avatar_split_clause,[],[f52,f223]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f221,plain,
spl0_4,
inference(avatar_split_clause,[],[f4,f219]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f217,plain,
spl0_3,
inference(avatar_split_clause,[],[f69,f214]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).
fof(f212,plain,
spl0_2,
inference(avatar_split_clause,[],[f50,f209]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f207,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f113,f204]) ).
fof(f113,axiom,
x != intersection(x,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idempotency_of_intersection_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET148-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.06/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri May 3 16:28:23 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % (2228)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (2231)WARNING: value z3 for option sas not known
% 0.14/0.37 % (2232)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (2233)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37 % (2234)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37 % (2229)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (2230)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (2235)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.37 % (2231)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.41 TRYING [1]
% 0.21/0.42 TRYING [2]
% 0.21/0.50 TRYING [3]
% 1.34/0.54 TRYING [1]
% 1.44/0.54 TRYING [2]
% 1.44/0.59 TRYING [4]
% 1.44/0.60 TRYING [1]
% 1.44/0.60 TRYING [2]
% 1.44/0.61 TRYING [3]
% 2.03/0.63 TRYING [3]
% 2.03/0.66 TRYING [4]
% 3.03/0.80 TRYING [5]
% 3.55/0.87 TRYING [5]
% 6.22/1.23 TRYING [6]
% 6.22/1.24 TRYING [4]
% 9.18/1.66 TRYING [6]
% 13.37/2.28 % (2233)First to succeed.
% 13.99/2.35 % (2233)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2228"
% 13.99/2.35 % (2233)Refutation found. Thanks to Tanya!
% 13.99/2.35 % SZS status Unsatisfiable for theBenchmark
% 13.99/2.35 % SZS output start Proof for theBenchmark
% See solution above
% 13.99/2.37 % (2233)------------------------------
% 13.99/2.37 % (2233)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 13.99/2.37 % (2233)Termination reason: Refutation
% 13.99/2.37
% 13.99/2.37 % (2233)Memory used [KB]: 25496
% 13.99/2.37 % (2233)Time elapsed: 1.975 s
% 13.99/2.37 % (2233)Instructions burned: 6175 (million)
% 13.99/2.37 % (2228)Success in time 2.014 s
%------------------------------------------------------------------------------